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The ContinuousTime Lace Expansion Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210904
David Brydges, Tyler Helmuth, Mark HolmesWe derive a continuoustime lace expansion for a broad class of selfinteracting continuoustime random walks. Our expansion applies when the selfinteraction is a sufficiently nice function of the local time of a continuoustime random walk. As a special case we obtain a continuoustime lace expansion for a class of spin systems that admit continuoustime random walk representations.

The Batchelor Spectrum of Passive Scalar Turbulence in Stochastic Fluid Mechanics at Fixed Reynolds Number Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210907
Jacob Bedrossian, Alex Blumenthal, Samuel PunshonSmithIn 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids with small diffusivity k should display a power spectrum along an inertial range contained in the viscousconvective range of the fluid model. This prediction has been extensively tested, both experimentally and numerically, and is a core prediction of passive scalar turbulence.

Plateau's Problem as a Singular Limit of Capillarity Problems Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210830
Darren King, Francesco Maggi, Salvatore StuvardSoap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection

Universality Near the Gradient Catastrophe Point in the Semiclassical SineGordon Equation Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210825
BingYing Lu, Peter MillerWe study the semiclassical limit of the sineGordon (sG) equation with below threshold pure impulse initial data of KlausShaw type. The Whitham averaged approximation of this system exhibits a gradient catastrophe in finite time. In accordance with a conjecture of Dubrovin, Grava, and Klein, we found that in a neighborhood near the gradient catastrophe point, the asymptotics of the sG solution are

Mathematical Modeling and Analysis of Spatial Neuron Dynamics: Dendritic Integration and Beyond Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210824
Songting Li, David W. McLaughlin, Douglas ZhouNeurons compute by integrating spatiotemporal excitatory (E) and inhibitory (I) synaptic inputs received from the dendrites. The investigation of dendritic integration is crucial for understanding neuronal information processing. Yet quantitative rules of dendritic integration and their mathematical modeling remain to be fully elucidated. Here neuronal dendritic integration is investigated by using

Uniformly Positive Correlations in the Dimer Model and Macroscopic Interacting SelfAvoiding Walk in , Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210818
Lorenzo TaggiOur first main result is that correlations between monomers in the dimer model in do not decay to 0 when . This is the first rigorous result about correlations in the dimer model in dimensions greater than 2 and shows that the model behaves drastically differently than in two dimensions, in which case it is integrable and correlations are known to decay to zero polynomially. Such a result is implied

Gaussian Regularization of the Pseudospectrum and Davies’ Conjecture Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210816
Jess Banks, Archit Kulkarni, Satyaki Mukherjee, Nikhil SrivastavaA matrix is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every is the limit of diagonalizable matrices. We prove a quantitative version of this fact conjectured by E. B. Davies: for each , every matrix is at least close to one whose eigenvectors have condition number at worst , for some depending only on n. We

EntropyBounded Solutions to the OneDimensional Heat Conductive Compressible NavierStokes Equations with Far Field Vacuum Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210802
Jinkai Li, Zhouping XinIn the presence of vacuum, the physical entropy for polytropic gases behave singularly, and it is thus a challenge to study its dynamics. It is shown in this paper that the boundedness of the entropy can be propagated up to any finite time provided that the initial vacuum presents only at far fields with sufficiently slow decay of the initial density. More precisely, for the Cauchy problem of the onedimensional

Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the ThreeBody Problem Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210729
Maciej J. Capiński, Marian GideaWe consider a class of autonomous Hamiltonian systems subject to small, timeperiodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation parameter is nonzero.

Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210722
Andrew Lawrie, Jonas Lührmann, SungJin Oh, Sohrab ShahshahaniWe consider the Cauchy problem for the Schrödinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studied case on the Euclidean plane is the existence of a rich new family of finite energy harmonic maps. These are stationary solutions, and thus play an important role in the dynamics of Schrödinger maps. The main result of this

Moderately Discontinuous Homology Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210722
Javier Fernández de Bobadilla, Sonja Heinze, María Pe Pereira, José Edson SampaioWe introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of metric singular subanalytic germs. The main novelty of our approach is to allow “moderately discontinuous” chains, which are specially advantageous for capturing the subtleties of the outer metric phenomena. Our invariant is a finitely generated graded abelian group

Minimizers for the Thin OnePhase Free Boundary Problem Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210716
Max Engelstein, Aapo Kauranen, Martí Prats, Georgios Sakellaris, Yannick SireWe consider the “thin onephase" free boundary problem, associated to minimizing a weighted Dirichlet energy of the function in plus the area of the positivity set of that function in . We establish full regularity of the free boundary for dimensions , prove almost everywhere regularity of the free boundary in arbitrary dimension, and provide content and structure estimates on the singular set of the

Upper Tail Large Deviations in First Passage Percolation Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210614
Riddhipratim Basu, Allan Sly, Shirshendu GangulyFor first passage percolation on with i.i.d. bounded edge weights, we consider the upper tail large deviation event, i.e., the rare situation where the first passage time between two points at distance n is macroscopically larger than typical. It was shown by Kesten [24] that the probability of this event decays as . However, the question of existence of the rate function, i.e., whether the logprobability

The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210606
Song Mei, Andrea MontanariDeep learning methods operate in regimes that defy the traditional statistical mindset. Neural network architectures often contain more parameters than training samples, and are so rich that they can interpolate the observed labels, even if the latter are replaced by pure noise. Despite their huge complexity, the same architectures achieve small generalization error on real data.

Mean Convex Mean Curvature Flow with Free Boundary Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210602
Nick Edelen, Robert Haslhofer, Mohammad N. Ivaki, Jonathan J. ZhuIn this paper, we generalize White's regularity and structure theory for meanconvex mean curvature flow [45, 46, 48] to the setting with free boundary. A major new challenge in the free boundary setting is to derive an a priori bound for the ratio between the norm of the second fundamental form and the mean curvature. We establish such a bound via the maximum principle for a tripleapproximation scheme

Spatially Inhomogeneous Evolutionary Games Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210513
Luigi Ambrosio, Massimo Fornasier, Marco Morandotti, Giuseppe SavaréWe introduce and study a mean‐field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the interaction between different players and return a feedback on the velocity field guiding their motion.

Quantitative Linearization Results for the Monge‐Ampère Equation Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210502
Michael Goldman, Martin Huesmann, Felix OttoThis paper is about quantitative linearization results for the Monge‐Ampère equation with rough data. We develop a large‐scale regularity theory and prove that if a measure μ is close to the Lebesgue measure in Wasserstein distance at all scales, then the displacement of the macroscopic optimal coupling is quantitatively close at all scales to the gradient of the solution of the corresponding Poisson

Finite Time Blowup for the Nematic Liquid Crystal Flow in Dimension Two Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210429
Chen‐Chih Lai, Fanghua Lin, Changyou Wang, Juncheng Wei, Yifu ZhouWe consider the initial boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain Ω ⊂ ℝ2. Given any k distinct points in the domain, we develop a new inner‐outer gluing method to construct solutions that blow up exactly at those k points as t goes to a finite time T. Moreover, we obtain a precise description of the blowup. © 2021 Wiley Periodicals LLC.

Quantitative Estimates for Regular Lagrangian Flows with BV Vector Fields Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210413
Quoc‐Hung NguyenThis paper is devoted to the study of flows associated to non‐smooth vector fields. We prove the well‐posedness of regular Lagrangian flows associated to vector fields B = (B1, …, Bd) ∈ L1(ℝ+; L1(ℝd) + L∞(ℝd)) satisfying bj ∈ L1(ℝ+, BV(ℝd)) and div(B) ∈ L1(ℝ+; L∞(ℝd)) for d, m ≥ 2, where are singular kernels in ℝd. Moreover, we also show that there exist an autonomous vector‐field B ∈ L1(ℝ2) + L∞(ℝ2)

On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210412
Jiajie Chen, Thomas Y. Hou, De HuangWe present a novel method of analysis and prove finite time asymptotically self‐similar blowup of the De Gregorio model [13, 14] for some smooth initial data on the real line with compact support. We also prove self‐similar blowup results for the generalized De Gregorio model [41] for the entire range of parameter on ℝ or for Hölder‐continuous initial data with compact support. Our strategy is to reformulate

Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210401
Björn Engquist, Yunan YangFull‐waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging. PDE‐constrained optimization is used to determine unknown parameters in a wave equation that represent geophysical properties. The objective function measures the misfit between the observed data and the calculated synthetic data, and it has traditionally been the least‐squares norm. In a sequence

Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210330
Wei‐Xi Li, Nader Masmoudi, Tong YangWe establish the well‐posedness in Gevrey function space with optimal class of regularity 2 for the three‐dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system. This shows that the three‐dimensional instabilities in the system leading

Refined Description and Stability for Singular Solutions of the 2D Keller‐Segel System Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210325
Charles Collot, Tej‐Eddine Ghoul, Nader Masmoudi, Van Tien NguyenWe construct solutions to the two‐dimensional parabolic‐elliptic Keller‐Segel model for chemotaxis that blow up in finite time T. The solution is decomposed as the sum of a stationary state concentrated at scale λ and of a perturbation. We rely on a detailed spectral analysis for the linearised dynamics in the parabolic neighbourhood of the singularity performed by the authors in [10], providing a

Liouville Theorems and a Schwarz Lemma for Holomorphic Mappings Between Kähler Manifolds Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210314
Lei NiWe derive some consequences of the Liouville theorem for plurisubharmonic functions of L.‐F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of ℂ isometrically from the simply connected Kähler manifold with nonnegative bisectional curvature and a linear growth holomorphic function) of L.‐F. Tam and the author. The second

Mean‐Field and Classical Limit for the N‐Body Quantum Dynamics with Coulomb Interaction Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210309
François Golse, Thierry PaulThis paper proves the validity of the joint mean‐field and classical limit of the bosonic quantum N‐body dynamics leading to the pressureless Euler‐Poisson system for factorized initial data whose first marginal has a monokinetic Wigner measure. The interaction potential is assumed to be the repulsive Coulomb potential. The validity of this derivation is limited to finite time intervals on which the

Long‐Term Regularity of 3D Gravity Water Waves Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210306
Fan ZhengWe study a fundamental model in fluid mechanics—the 3D gravity water wave equation, in which an incompressible fluid occupying half the 3D space flows under its own gravity. In this paper we show long‐term regularity of solutions whose initial data is small but not localized.

Variational Embedding for Quantum Many‐Body Problems Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210227
Lin Lin, Michael LindseyQuantum embedding theories are powerful tools for approximately solving large‐scale, strongly correlated quantum many‐body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale and a less accurate quantum theory at the global scale. We introduce the first quantum embedding theory that is also variational, in that it is guaranteed to provide

A Remark on the Concentration Compactness Principle in Critical Dimension Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210226
Fengbo HangWe prove some refinements of the concentration compactness principle for Sobolev space W1, n on a smooth compact Riemannian manifold of dimension n. As an application, we extend Aubin's theorem for functions on with zero first‐order moments of the area element to the higher‐order moments case. Our arguments are very flexible and can be easily modified for functions satisfying various boundary conditions

Multitime Distribution in Discrete Polynuclear Growth Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210222
Kurt Johansson, Mustazee RahmanWe study the multitime distribution in a discrete polynuclear growth model or, equivalently, in directed last‐passage percolation with geometric weights. A formula for the joint multitime distribution function is derived in the discrete setting. It takes the form of a multiple contour integral of a block Fredholm determinant. The asymptotic multitime distribution is then computed by taking the appropriate

Local Flexibility for Open Partial Differential Relations Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210221
Christian Bär, Bernhard HankeWe show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian

Coagulation‐Fragmentation Equations with Multiplicative Coagulation Kernel and Constant Fragmentation Kernel Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210221
Hung V. Tran, Truong‐Son VanWe study a critical case of coagulation‐fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the study of viscosity solutions to a new singular Hamilton‐Jacobi equation, which results from applying the Bernstein transform to the original coagulation‐fragmentation equation. Our results include well‐posedness, regularity, and long‐time

Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210213
Otis Chodosh, Michael Eichmair, Yuguang Shi, Haobin YuLet (M, g) be an asymptotically flat Riemannian 3‐manifold with nonnegative scalar curvature and positive mass. We show that each leaf of the canonical foliation of the end of (M, g) through stable constant mean curvature spheres encloses more volume than any other surface of the same area.

A Riemann‐Hilbert Approach to the Lower Tail of the Kardar‐Parisi‐Zhang Equation Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210124
Mattia Cafasso, Tom ClaeysFredholm determinants associated to deformations of the Airy kernel are closely connected to the solution to the Kardar‐Parisi‐Zhang (KPZ) equation with narrow wedge initial data, and they also appear as largest particle distributions in models of positive‐temperature free fermions.

Fast Computation of Orthogonal Systems with a Skew‐Symmetric Differentiation Matrix Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210117
Arieh Iserles, Marcus WebbOrthogonal systems in L2(ℝ), once implemented in spectral methods, enjoy a number of important advantages if their differentiation matrix is skew‐symmetric and highly structured. Such systems, where the differentiation matrix is skew‐symmetric, tridiagonal, and irreducible, have been recently fully characterised. In this paper we go a step further, imposing the extra requirement of fast computation:

The One‐Dimensional Log‐Gas Free Energy Has a Unique Minimizer Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210117
Matthias Erbar, Martin Huesmann, Thomas LebléWe prove that, at every positive temperature, the infinite‐volume free energy of the one‐dimensional log‐gas, or beta‐ensemble, has a unique minimizer, which is the Sine‐beta process arising from random matrix theory. We rely on a quantitative displacement convexity argument at the level of point processes, and on the screening procedure introduced by Sandier‐Serfaty. © 2020 Wiley Periodicals, Inc

Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210114
Alexandru Ionescu, Hao JiaWe prove asymptotic stability of point vortex solutions to the full Euler equation in two dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported perturbation of a point vortex leads to a global solution of the Euler equation in 2D, which converges weakly as t → ∞ to a radial profile with respect to the vortex. The position of the point vortex, which is time dependent

A Control Variate Method Driven by Diffusion Approximation Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210114
Josselin Garnier, Laurent MertzIn this paper we introduce a control variate estimator for a quantity of interest that can be expressed as the expectation of a function of a random process, that is itself the solution of a differential equation driven by fast mean‐reverting ergodic random forces. The control variate is built with the same function and with the limit diffusion process that approximates the original random process

The Data‐Driven Schrödinger Bridge Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20210114
Michele Pavon, Giulio Trigila, Esteban G. TabakErwin Schrödinger posed—and to a large extent solved—in 1931/32 the problem of finding the most likely random evolution between two continuous probability distributions. This article considers this problem in the case when only samples of the two distributions are available. A novel iterative procedure is proposed, inspired by Fortet‐IPF‐Sinkhorn type algorithms. Since only samples of the marginals

Conditional Density Estimation, Latent Variable Discovery, and Optimal Transport Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201228
Hongkang Yang, Esteban G. TabakA framework is proposed that addresses both conditional density estimation and latent variable discovery. The objective function maximizes explanation of variability in the data, achieved through the optimal transport barycenter generalized to a collection of conditional distributions indexed by a covariate either given or latent in any suitable space. Theoretical results establish the existence

A Scalar Version of the Caflisch‐Luke Paradox Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201221
Antoine GloriaConsider an infinite cloud of hard spheres sedimenting in a Stokes flow in the whole space $\mathbb R^d$. Despite many contributions in fluid mechanics and applied mathematics, there is so far no rigorous definition of the associated effective sedimentation velocity. Calculations by Caflisch and Luke in dimension $d=3$ suggest that the effective velocity is welldefined for hard spheres distributed

AlmostRigidity of Frameworks Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201219
Miranda HolmesCerfon, Louis Theran, Steven J. GortlerWe extend the mathematical theory of rigidity of frameworks (graphs embedded in ddimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes continuously it must remain inside a small ball, a property we call “almostrigidity”; (II) any other framework with the same edge lengths must lie outside a much larger

Regularized Stokes Immersed Boundary Problems in Two Dimensions: Well‐Posedness , Singular Limit, and Error Estimates Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201214
Jiajun TongInspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1D closed elastic string in a 2D Stokes flow, in which a regularized $\delta$function is used to mollify the flow field and singular forcing. We establish global wellposedness of the regularized problems, and prove that as the regularization

Cycle Class Maps and Birational Invariants Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201212
Brendan Hassett, Yuri TschinkelWe introduce new obstructions to rationality for geometrically rational threefolds arising from the geometry of curves and their cycle maps.

The Quasi Curvature‐Dimension Condition with Applications to Sub‐Riemannian Manifolds Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201212
Emanuel MilmanWe obtain the best known quantitative estimates for the $L^p$Poincare and logSobolev inequalities on domains in various subRiemannian manifolds, including ideal Carnot groups and in particular ideal generalized Htype Carnot groups and the Heisenberg groups, corank $1$ Carnot groups, the Grushin plane, and various Htype foliations, Sasakian and $3$Sasakian manifolds. Moreover, this constitutes

On Admissible Locations of Transonic Shock Fronts for Steady Euler Flows in an Almost Flat Finite Nozzle with Prescribed Receiver Pressure Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201209
Beixiang Fang, Zhouping XinThis paper concerns the existence of transonic shock solutions to the 2D steady compressible Euler system in an almost flat finite nozzle ( in the sense that it is a generic small perturbation of a flat one ), under physical boundary conditions proposed by CourantFriedrichs in \cite{CourantFriedrichs1948}, in which the receiver pressure is prescribed at the exit of the nozzle. In the resulting free

Area‐Minimizing Currents mod 2 Q : Linear Regularity Theory Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201130
Camillo De Lellis, Jonas Hirsch, Andrea Marchese, Salvatore StuvardWe establish a theory of $Q$valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents $\mathrm{mod}(p)$ when $p=2Q$, and to establish a first general partial regularity theorem for every $p$ in any dimension and codimension.

Averaging Principle and Shape Theorem for a Growth Model with Memory Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201129
Amir Dembo, Pablo Groisman, Ruojun Huang, Vladas SidoraviciusWe present a general approach to study a class of random growth models in $n$dimensional Euclidean space. These models are designed to capture basic growth features which are expected to manifest at the mesoscopic level for several classical selfinteracting processes originally defined at the microscopic scale. It includes oncereinforced random walk with strong reinforcement, originexcited random

DLR Equations and Rigidity for the Sine‐Beta Process Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201118
David Dereudre, Adrien Hardy, Thomas Leblé, Mylène MaïdaWe investigate Sine$_\beta$, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of onedimensional loggases, or $\beta$ensembles, at inverse temperature $\beta>0$. We adopt a statistical physics perspective, and give a description of Sine$_\beta$ using the DobrushinLanfordRuelle (DLR) formalism by proving that it satisfies the DLR equations:

Minimal Surfaces in Hyperbolic 3‐Manifolds Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201104
Baris CoskunuzerIn this paper, we show the existence of smoothly embedded closed minimal surfaces in infinite volume hyperbolic $3$manifolds except some special cases.

Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201104
Shmuel Weinberger, Zhizhang Xie, Guoliang YuLet $X$ be a closed oriented connected topological manifold of dimension $n\geq 5$. The structure group of $X$ is the abelian group of equivalence classes of all pairs $(f, M)$ such that $M$ is a closed oriented manifold and $f\colon M \to X$ is an orientationpreserving homotopy equivalence. The main purpose of this article is to prove that a higher rho invariant defines a group homomorphism from

Maximum and Shape of Interfaces in 3D Ising Crystals Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201101
Reza Gheissari, Eyal LubetzkyDobrushin (1972) showed that the interface of a 3D Ising model with minus boundary conditions above the $xy$plane and plus below is rigid (has $O(1)$fluctuations) at every sufficiently low temperature. Since then, basic features of this interface  such as the asymptotics of its maximum  were only identified in more tractable random surface models that approximate the Ising interface at low temperatures

On the Convex Geometry of Blind Deconvolution and Matrix Completion Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201029
Felix Krahmer, Dominik StögerLowrank matrix recovery from structured measurements has been a topic of intense study in the last decade and many important problems like matrix completion and blind deconvolution have been formulated in this framework. An important benchmark method to solve these problems is to minimize the nuclear norm, a convex proxy for the rank. A common approach to establish recovery guarantees for this convex

Formation of Shocks for 2D Isentropic Compressible Euler Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201027
Tristan Buckmaster, Steve Shkoller, Vlad VicolWe consider the 2D isentropic compressible Euler equations, with pressure law $p(\rho) = (\sfrac{1}{\gamma}) \rho^\gamma$, with $\gamma >1$. We provide an elementary constructive proof of shock formation from smooth initial datum of finite energy, with no vacuum regions, and with {nontrivial vorticity}. We prove that for initial data which has minimum slope $ {\sfrac{1}{ \eps}}$, for $ \eps>0$ taken

Large‐Scale Analyticity and Unique Continuation for Periodic Elliptic Equations Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201027
Scott Armstrong, Tuomo Kuusi, Charles SmartWe prove that a solution of an elliptic operator with periodic coefficients behaves on large scales like an analytic function, in the sense of approximation by polynomials with periodic corrections. Equivalently, the constants in the largescale $C^{k,1}$ estimate scale exponentially in $k$, just as for the classical estimate for harmonic functions. As a consequence, we characterize entire solutions

A High‐Order Integral Equation‐Based Solver for the Time‐Dependent Schrödinger Equation Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201027
Jason Kaye, Alex Barnett, Leslie GreengardWe introduce a numerical method for the solution of the timedependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary conditions, and for free space problems with compactly supported initial data and potential. A spatially uniform electric field may be included, making the solver

Robustness of Liouville Measure under a Family of Stable Diffusions Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20200825
François Ledrappier, Lin ShuConsider a C∞ closed connected Riemannian manifold (M, g) with negative sectional curvature. The unit tangent bundle SM is foliated by the (weak) stable foliation of the geodesic flow. Let Δs be the leafwise Laplacian for and let X be the geodesic spray, i.e., the vector field that generates the geodesic flow. For each ρ, the operator generates a diffusion for . We show that, as ρ → − ∞, the unique

Unique Asymptotics of Compact Ancient Solutions to Three‐Dimensional Ricci Flow Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201016
Sigurd Angenent, Simon Brendle, Panagiota Daskalopoulos, Natasa ŠešumWe consider compact ancient solutions to the threedimensional Ricci flow which are noncollapsed. We prove that such a solutions is either a family of shrinking round spheres, or it has a unique asymptotic behavior as $t \to \infty$ which we describe. This analysis applies in particular to the ancient solution constructed by Perelman.

Refined Asymptotic Behavior of Blowup Solutions to a Simplified Chemotaxis System Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201011
Noriko MizoguchiWe deal with a parabolic‐elliptic chemotaxis system. It is known that finite‐time blowup occurs for a large class of initial data. However, there have been no results on exact blowup rate or detailed blowup behavior except a special radial solution given just formally in [13] and rigorously in [19, 10, 9]. Our aim is to show that for all radial blowup solutions, their blowup rate, and blowup profile

Plateau's Problem as a Singular Limit of Capillarity Problems Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201011
Darren King, Francesco Maggi, Salvatore StuvardSoap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection

Improved Moser‐Trudinger‐Onofri Inequality under Constraints Comm. Pure Appl. Math. (IF 3.219) Pub Date : 20201011
Sun‐Yung A. Chang, Fengbo HangA classical result of Aubin states that the constant in MoserTrudingerOnofri inequality on $\mathbb{S}^{2}$ can be imporved for furnctions with zero first order moments of the area element. We generalize it to higher order moments case. These new inequalities bear similarity to a sequence of LebedevMilin type inequalities on $\mathbb{S}^{1}$ coming from the work of GrenanderSzego on Toeplitz determinants