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  • Integral geometry of exceptional spheres
    J. Differ. Geom. (IF 2.167) Pub Date : 2021-01-06
    Gil Solanes; Thomas Wannerer

    The algebras of valuations on $S^6$ and $S^7$ invariant under the actions of $G_2$ and $\operatorname{Spin}(7)$ are shown to be isomorphic to the algebra of translation-invariant valuations on the tangent space at a point invariant under the action of the isotropy group. This is in analogy with the cases of real and complex space forms, suggesting the possibility that the same phenomenon holds in all

    更新日期:2021-01-06
  • Allen–Cahn min-max on surfaces
    J. Differ. Geom. (IF 2.167) Pub Date : 2021-01-06
    Christos Mantoulidis

    We use a min-max procedure on the Allen–Cahn energy functional to construct geodesics on closed, $2$‑dimensional Riemannian manifolds, as motivated by the work of Guaraco [Gua18]. Borrowing classical blowup and curvature estimates from geometric analysis, as well as novel Allen–Cahn curvature estimates due to Wang–Wei [WW19], we manage to study the fine structure of potential singular points at the

    更新日期:2021-01-06
  • Correspondence theorem between holomorphic discs and tropical discs on K3 surfaces
    J. Differ. Geom. (IF 2.167) Pub Date : 2021-01-06
    Yu-Shen Lin

    In this paper, we prove that the open Gromov–Witten invariants defined in [20] on K3 surfaces satisfy the Kontsevich–Soibelman wall-crossing formula. One hand, this gives a geometric interpretation of the slab functions in Gross–Siebert program. On the other hands, the open Gromov–Witten invariants coincide with the weighted counting of tropical discs. This is an analog of the corresponding theorem

    更新日期:2021-01-06
  • A construction of infinitely many solutions to the Strominger system
    J. Differ. Geom. (IF 2.167) Pub Date : 2021-01-06
    Teng Fei; Zhijie Huang; Sebastien Picard

    Teng Fei, Zhijie Huang, Sebastien Picard. Source: Journal of Differential Geometry, Volume 117, Number 1, 23--39.

    更新日期:2021-01-06
  • Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$
    J. Differ. Geom. (IF 2.167) Pub Date : 2021-01-06
    R. L. Bryant; P. Foulon; S. V. Ivanov; V. S. Matveev; W. Ziller

    We study non-reversible Finsler metrics with constant flag curvature $1$ on $S^2$ and show that the geodesic flow of every such metric is conjugate to that of one of Katok’s examples, which form a 1-parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metric with

    更新日期:2021-01-06
  • Index to Volume 126
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-12-03

    Source: Journal of Differential Geometry, Volume 116, Number 3

    更新日期:2020-12-03
  • The $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-12-03
    Zou Du; Xiong Ge

    Existence and uniqueness of the solution to the $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity are proved when $p \gt 1$ and $1 \lt \mathfrak{p} \lt n$. These results are nonlinear extensions of the very recent solution to the $L_p$ Minkowski problem for $\mathfrak{p}$-capacity when $p = 1$ and $1 \lt \mathfrak{p} \lt n$ by Colesanti et al. and Akman et al., and the classical

    更新日期:2020-12-03
  • New proof for the regularity of Monge–Ampère type equations
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-12-03
    Xu-Jia Wang; Yating Wu

    By employing the Green function, in this paper we provide a new and elementary proof for the interior regularity of solutions to the Monge–Ampère equation. This proof also applies to the complex Monge–Ampère equation and the $k$-Hessian equation.

    更新日期:2020-12-03
  • Linear stability of Schwarzschild spacetime: Decay of metric coefficients
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-12-03
    Pei-Ken Hung; Jordan Keller; Mu-Tao Wang

    In this paper, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, remain uniformly bounded and decay to a linearized Kerr metric on the exterior region

    更新日期:2020-12-03
  • Uniqueness of immersed spheres in three-manifolds
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-12-03
    José A. Gálvez; Pablo Mira

    In this paper we solve two open problems of classical surface theory; we give an affirmative answer to a 1956 conjecture by A.D. Alexandrov on the uniqueness of immersed spheres in $\mathbb{R}^3$ that satisfy a general elliptic prescribed curvature equation, and we prove as a consequence that round spheres are the only elliptic Weingarten spheres immersed in $\mathbb{R}^3$. For this, we first extend

    更新日期:2020-12-03
  • Basmajian-type inequalities for maximal representations
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-12-03
    Federica Fanoni; Maria Beatrice Pozzetti

    For suitable metrics on the locally symmetric space associated to a maximal representation, we prove inequalities between the length of the boundary and the lengths of orthogeodesics that generalize the classical Basmajian’s identity from Teichmüller theory. Any equality characterizes diagonal embeddings.

    更新日期:2020-12-03
  • Rational curves on general type hypersurfaces
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-10-29
    Eric Riedl; David Yang

    We develop a technique that allows us to prove results about subvarieties of general type hypersurfaces. As an application, we use a result of Clemens and Ran to prove that a very general hypersurface of degree $\frac{3n+1}{2} \leq d \leq 2n - 3$ in $\mathbb{P}^n$ contain lines but no other rational curves.

    更新日期:2020-10-30
  • On the moduli space of flat symplectic surface bundles
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-10-29
    Sam Nariman

    In this paper, we prove homological stability of symplectomorphisms and extended hamiltonians of surfaces made discrete. Similar to discrete surface diffeomorphisms [Nar17b], we construct an isomorphism from the stable homology group of symplectomorphisms and extended Hamiltonians of surfaces to the homology of certain infinite loop spaces. We use these infinite loop spaces to study characteristic

    更新日期:2020-10-30
  • Limits of $\alpha$-harmonic maps
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-10-29
    Tobias Lamm; Andrea Malchiodi; Mario Micallef

    Critical points of approximations of the Dirichlet energy à la Sacks–Uhlenbeck are known to converge to harmonic maps in a suitable sense. However, we show that not every harmonic map can be approximated by critical points of such perturbed energies. Indeed, we prove that constant maps and maps of the form $u^R (x) = Rx, R \in O(3)$, are the only critical points of $E_\alpha$ for maps from $S^2$ to

    更新日期:2020-10-30
  • Limiting behavior of sequences of properly embedded minimal disks
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-10-29
    David Hoffman; Brian White

    We develop a theory of “minimal $\theta$-graphs” and characterize the behavior of limit laminations of such surfaces, including an understanding of their limit leaves and their curvature blow-up sets. We use this to prove that it is possible to realize families of catenoids in euclidean space as limit leaves of sequences of embedded minimal disks, even when there is no curvature blow-up. Our methods

    更新日期:2020-10-30
  • Rank 2 affine manifolds in genus $3$
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-10-29
    David Aulicino; Duc-Manh Nguyen

    We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.

    更新日期:2020-10-30
  • The Kähler–Ricci flow and optimal degenerations
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-09-05
    Ruadhaí Dervan; Gábor Székelyhidi

    We prove that on Fano manifolds, the Kähler–Ricci flow produces a “most destabilising” degeneration, with respect to a new stability notion related to the $H$-functional. This answers questions of Chen–Sun–Wang and He. We give two applications of this result. Firstly, we give a purely algebro-geometric formula for the supremum of Perelman’s $\mu$‑functional on Fano manifolds, resolving a conjecture

    更新日期:2020-09-07
  • Regularity theory for $2$-dimensional almost minimal currents III: Blowup
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-09-05
    Camillo De Lellis; Emanuele Spadaro; Luca Spolaor

    We analyze the asymptotic behavior of a $2$-dimensional integral current which is almost minimizing in a suitable sense at a singular point. Our analysis is the second half of an argument which shows the discreteness of the singular set for the following three classes of $2$-dimensional currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of $3$-dimensional

    更新日期:2020-09-07
  • Space of Ricci flows (II)—Part B: Weak compactness of the flows
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-09-05
    Xiuxiong Chen; Bing Wang

    Based on the compactness of the moduli of non-collapsed Calabi–Yau spaces with mild singularities, we set up a structure theory for polarized Kähler Ricci flows with proper geometric bounds. Our theory is a generalization of the structure theory of non-collapsed Kähler Einstein manifolds. As applications, we show the convergence of the Kähler Ricci flow in an appropriate topology and prove the par

    更新日期:2020-09-07
  • Index to Volume 115
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-07-09

    Source: Journal of Differential Geometry, Volume 115, Number 3

    更新日期:2020-07-20
  • Totally geodesic submanifolds of Teichmüller space
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-07-09
    Alex Wright

    Let $\mathcal{T}_{g,n}$ and $\mathcal{M}_{g,n}$ denote the Teichmüller and moduli space respectively of genus $g$ Riemann surfaces with $n$ marked points. The Teichmüller metric on these spaces is a natural Finsler metric that quantifies the failure of two different Riemann surfaces to be conformally equivalent. It is equal to the Kobayashi metric [Roy74], and hence reflects the intrinsic complex geometry

    更新日期:2020-07-20
  • Chern–Ricci flows on noncompact complex manifolds
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-07-09
    Man-Chun Lee; Luen-Fai Tam

    In this work, we obtain existence criteria for Chern–Ricci flows on noncompact manifolds. We generalize a result by Tossati–Wienkove [37] on Chern-Ricci flows to noncompact manifolds and a result for Kähler–Ricci flows by Lott–Zhang [21] to Chern–Ricci flows. Using the existence results, we prove that any complete noncollapsed Kähler metric with nonnegative bisectional curvature on a noncompact complex

    更新日期:2020-07-20
  • Deligne pairings and families of rank one local systems on algebraic curves
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-07-09
    Gerard Freixas i Montplet; Richard A. Wentworth

    For smooth families $\mathcal{X} \to S$ of projective algebraic curves and holomorphic line bundles $\mathcal{L, M} \to X$ equipped with flat relative connections, we prove the existence of a canonical and functorial “intersection” connection on the Deligne pairing $\langle \mathcal{L, M} \rangle \to S$. This generalizes the construction of Deligne in the case of Chern connections of hermitian structures

    更新日期:2020-07-20
  • Variation of complex structures and variation of Lie algebras II: new Lie algebras arising from singularities
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-07-09
    Bingyi Chen; Naveed Hussain; Stephen S.-T. Yau; Huaiqing Zuo

    Finite dimensional Lie algebras are semi-direct product of the semi-simple Lie algebras and solvable Lie algebras. Brieskorn gave the connection between simple Lie algebras and simple singularities. Simple Lie algebras have been well understood, but not the solvable (nilpotent) Lie algebras. It is extremely important to establish connections between singularities and solvable (nilpotent) Lie algebras

    更新日期:2020-07-20
  • Riemann–Hilbert problems for the resolved conifold and non-perturbative partition functions
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-07-09
    Tom Bridgeland

    We study the Riemann-Hilbert problems of [6] (T. Bridgeland, “Riemann-Hilbert problems from Donaldson–Thomas theory”, arxiv:1611.03697) in the case of the Donaldson–Thomas theory of the resolved conifold. We give explicit solutions in terms of the Barnes double and triple sine functions. We show that the $\tau$-function of [6] is a non-perturbative partition function, in the sense that its asymptotic

    更新日期:2020-07-20
  • Minimizing cones associated with isoparametric foliations
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-05-19
    Zizhou Tang; Yongsheng Zhang

    Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces − minimal isoparametric hypersurfaces and focal submanifolds. By virtue of their rich structures, we find new series of minimizing cones. They are cones over focal submanifolds and cones over suitable products among these two classes. Except in low dimensions, all such cones are shown minimizing.

    更新日期:2020-07-20
  • Expanding Kähler–Ricci solitons coming out of Kähler cones
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-05-19
    Ronan J. Conlon; Alix Deruelle

    We give necessary and sufficient conditions for a Kähler equivariant resolution of a Kähler cone, with the resolution satisfying one of a number of auxiliary conditions, to admit a unique asymptotically conical (AC) expanding gradient Kähler–Ricci soliton. In particular, it follows that for any $n \in \mathbb{N}_0$ and for any negative line bundle $L$ over a compact Kähler manifold $D$, the total space

    更新日期:2020-07-20
  • Isoparametric hypersurfaces with four principal curvatures, IV
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-05-19
    Quo-Shin Chi

    We prove that an isoparametric hypersurface with four principal curvatures and multiplicity pair $(7, 8)$ is either the one constructed by Ozeki and Takeuchi, or one of the two constructed by Ferus, Karcher, and Münzner. This completes the classification of isoparametric hypersurfaces in spheres that É. Cartan initiated in the late 1930s.

    更新日期:2020-07-20
  • The nonexistence of negative weight derivations on positive dimensional isolated singularities: Generalized Wahl conjecture
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-05-19
    Bingyi Chen; Hao Chen; Stephen S.-T. Yau; Huaiqing Zuo

    Let $R = \mathbb{C} [ x_1, x_2, \dotsc , x_n ] / (f)$ where $f$ is a weighted homogeneous polynomial defining an isolated singularity at the origin. Then $R$ and $\operatorname{Der} (R,R)$ are graded. It is well-known that $\operatorname{Der} (R,R)$ does not have a negatively graded component. Wahl conjectured that this is still true for $R = \mathbb{C} [ x_1, x_2, \dotsc, x_n] / (f_1, f_2, \dotsc

    更新日期:2020-07-20
  • On the global rigidity of sphere packings on $3$-dimensional manifolds
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-04-07
    Xu Xu

    In this paper, we prove the global rigidity of sphere packings on $3$-dimensional manifolds. This is a $3$-dimensional analogue of the rigidity theorem of Andreev–Thurston and was conjectured by Cooper and Rivin in [5]. We also prove a global rigidity result using a combinatorial scalar curvature introduced by Ge and the author in [13].

    更新日期:2020-04-07
  • The reverse Yang–Mills–Higgs flow in a neighbourhood of a critical point
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-04-07
    Graeme Wilkin

    The main result of this paper is a construction of solutions to the reverse Yang–Mills–Higgs flow converging in the $C^{\infty}$ topology to a critical point. The construction uses only the complex gauge group action, which leads to an algebraic classification of the isomorphism classes of points in the unstable set of a critical point in terms of a filtration of the underlying Higgs bundle. Analysing

    更新日期:2020-04-07
  • An intrinsic hyperboloid approach for Einstein Klein–Gordon equations
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-04-07
    Qian Wang

    Klainerman introduced in [7] the hyperboloidal method to prove global existence results for nonlinear Klein–Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to Lorentzian spacetimes. This approach is developed in [15] for proving, under the maximal foliation gauge, the global nonlinear stability of Minkowski space for Einstein

    更新日期:2020-04-07
  • The catenoid estimate and its geometric applications
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-04-07
    Daniel Ketover; Fernando C. Marques; André Neves

    We prove a sharp area estimate for catenoids that allows us to rule out the phenomenon of multiplicity in min-max theory in several settings. We apply it to prove that i) the width of a three-manifold with positive Ricci curvature is realized by an orientable minimal surface ii) minimal genus Heegaard surfaces in such manifolds can be isotoped to be minimal and iii) the “doublings” of the Clifford

    更新日期:2020-04-07
  • Index to Volume 114
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-03-05

    Source: Journal of Differential Geometry, Volume 114, Number 3

    更新日期:2020-03-05
  • On the entropy of closed hypersurfaces and singular self-shrinkers
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-03-05
    Jonathan J. Zhu

    Self-shrinkers are the special solutions of mean curvature flow in $\mathbf{R}^{n+1}$ that evolve by shrinking homothetically; they serve as singularity models for the flow. The entropy of a hypersurface introduced by Colding–Minicozzi is a Lyapunov functional for the mean curvature flow, and is fundamental to their theory of generic mean curvature flow. In this paper we prove that a conjecture of

    更新日期:2020-03-05
  • Minimal surfaces in the $3$-sphere by stacking Clifford tori
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-03-05
    David Wiygul

    Extending work of Kapouleas and Yang, for any integers $N \geq 2, {k , \ell} \geq 1$, and m sufficiently large, we apply gluing methods to construct in the round $3$-sphere a closed embedded minimal surface that has genus ${k \ell m}^2 (N-1)+1$ and is invariant under a $D_{km} \times D_{\ell m}$ subgroup of $O(4)$, where $D_n$ is the dihedral group of order $2n$. Each such surface resembles the union

    更新日期:2020-03-05
  • Floer theory for Lagrangian cobordisms
    J. Differ. Geom. (IF 2.167) Pub Date : 2020-03-05
    Baptiste Chantraine; Georgios Dimitroglou Rizell; Paolo Ghiggini; Roman Golovko

    In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the Chekanov–Eliashberg algebras of the negative ends of the cobordisms admit augmentations. From this theory we derive several long exact sequences relating the Morse homology of an exact Lagrangian cobordism with the bilinearised

    更新日期:2020-03-05
  • Extremal metrics on blowups along submanifolds
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-12-28
    Reza Seyyedali; Gábor Székelyhidi

    We give conditions under which the blowup of an extremal Kähler manifold along a submanifold of codimension greater than two admits an extremal metric. This generalizes work of Arezzo–Pacard–Singer, who considered blowups in points.

    更新日期:2019-12-28
  • The Ricci flow on the sphere with marked points
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-12-28
    D. H. Phong; Jian Song; Jacob Sturm; Xiaowei Wang

    The Ricci flow on the $2$-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is given. The semistable and unstable cases are new, and it is shown that the flow converges in the Gromov–Hausdorff topology to a limiting metric space which is also

    更新日期:2019-12-28
  • Hodge-theoretic mirror symmetry for toric stacks
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-12-28
    Tom Coates; Alessio Corti; Hiroshi Iritani; Hsian-Hua Tseng

    Using the mirror theorem [15], we give a Landau–Ginzburg mirror description for the big equivariant quantum cohomology of toric Deligne–Mumford stacks. More precisely, we prove that the big equivariant quantum $D$-module of a toric Deligne–Mumford stack is isomorphic to the Saito structure associated to the mirror Landau–Ginzburg potential. We give a Gelfand–Kapranov–Zelevinsky (GKZ) style presentation

    更新日期:2019-12-28
  • Rational curves on compact Kähler manifolds
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-12-28
    Junyan Cao; Andreas Höring

    Mori’s theorem yields the existence of rational curves on projective manifolds such that the canonical bundle is not nef. In this paper we study compact Kähler manifolds such that the canonical bundle is pseudoeffective, but not nef. We present an inductive argument for the existence of rational curves that uses neither deformation theory nor reduction to positive characteristic. The main tool for

    更新日期:2019-12-28
  • Index to Volume 113
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-11-15

    Source: Journal of Differential Geometry, Volume 113, Number 3

    更新日期:2019-11-15
  • Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-11-15
    Siyuan Lu; Pengzi Miao

    On a compact Riemannian manifold with boundary having positive mean curvature, a fundamental result of Shi and Tam states that, if the manifold has nonnegative scalar curvature and if the boundary is isometric to a strictly convex hypersurface in the Euclidean space, then the total mean curvature of the boundary is no greater than the total mean curvature of the corresponding Euclidean hypersurface

    更新日期:2019-11-15
  • An integral formula and its applications on sub-static manifolds
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-11-15
    Junfang Li; Chao Xia

    In this article, we first establish the main tool—an integral formula (1.1) for Riemannian manifolds with multiple boundary components (or without boundary). This formula generalizes Reilly’s original formula from [15] and the recent result from [17]. It provides a robust tool for sub-static manifolds regardless of the underlying topology. Using (1.1) and suitable elliptic PDEs, we prove Heintze–Karcher

    更新日期:2019-11-15
  • Real Gromov–Witten theory in all genera and real enumerative geometry: computation
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-11-15
    Penka Georgieva; Aleksey Zinger

    Gromov–Witten invariants of real-orientable symplectic manifolds of odd “complex” dimensions; the second part studies the orientations on the moduli spaces of real maps used in constructing these invariants. The present paper applies the results of the latter to obtain quantitative and qualitative conclusions about the invariants defined in the former. After describing large collections of real-orientable

    更新日期:2019-11-15
  • Codimension two holomorphic foliation
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-11-15
    Dominique Cerveau; A. Lins Neto

    This paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Conversely we show the existence of codimension two foliations which are not contained in any codimension one foliation. We study problems related to the singular locus and we classify homogeneous

    更新日期:2019-11-15
  • Convex $\mathbb{RP}^2$ structures and cubic differentials under neck separation
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-10-24
    John Loftin

    Let $S$ be a closed oriented surface of genus at least two. Labourie and the author have independently used the theory of hyperbolic affine spheres to find a natural correspondence between convex $\mathbb{RP}^2$ structures on $S$ and pairs $(\Sigma, U)$ consisting of a conformal structure $\Sigma$ on $S$ and a holomorphic cubic differential $U$ over $\Sigma$. We consider geometric limits of convex

    更新日期:2019-10-24
  • Plurisubharmonic envelopes and supersolutions
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-10-24
    Vincent Guedj; Chinh H. Lu; Ahmed Zeriahi

    We make a systematic study of (quasi-)plurisubharmonic envelopes on compact Kähler manifolds, as well as on domains of $\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber19]. We show that the quasi-plurisubharmonic envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge–Ampère equation. We use these ideas to solve complex Monge–Ampère

    更新日期:2019-10-24
  • Quantitative volume space form rigidity under lower Ricci curvature bound I
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-10-24
    Lina Chen; Xiaochun Rong; Shicheng Xu

    Let $M$ be a compact $n$-manifold of $\mathrm{Ric}_M \geq (n - 1) H$ ($H$ is a constant). We are concerned with the following space form rigidity: $M$ is isometric to a space form of constant curvature $H$ under either of the following conditions: (i) There is $ \rho \gt 0$ such that for any $x \in M$, the open $ \rho $-ball at $x^{\ast}$ in the (local) Riemannian universal covering space, $ (U^{\ast}_{\rho}

    更新日期:2019-10-24
  • Critical points of the classical Eisenstein series of weight two
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-10-24
    Zhijie Chen; Chang-Shou Lin

    In this paper, we completely determine the critical points of the normalized Eisenstein series $E_{2}(\tau)$ of weight 2. Although $E_{2}(\tau)$ is not a modular form, our result shows that $E_{2}(\tau)$ has at most one critical point in every fundamental domain of the form $\gamma (F_{0})$ of $\Gamma_{0}(2)$, where $\gamma (F_{0})$ are translates of the basic fundamental domain $F_{0}$ via the Möbius

    更新日期:2019-10-24
  • Maximizing Steklov eigenvalues on surfaces
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-08-31
    Romain Petrides

    We study the Steklov eigenvalue functionals $\sigma_k (\Sigma, g) L_g (\partial \Sigma)$ on smooth surfaces with non-empty boundary. We prove that, under some natural gap assumptions, these functionals do admit maximal metrics which come with an associated minimal surface with free boundary from $\Sigma$ into some Euclidean ball, generalizing previous results by Fraser and Schoen in [“Sharp eigenvalue

    更新日期:2019-08-31
  • Stable blowup for the supercritical Yang–Mills heat flow
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-08-31
    Roland Donninger; Birgit Schörkhuber

    In this paper, we consider the heat flow for Yang–Mills connections on $\mathbb{R}^5 \times SO(5)$. In the $SO(5)$-equivariant setting, the Yang–Mills heat equation reduces to a single semilinear reaction-diffusion equation for which an explicit self-similar blowup solution was found by Weinkove [“Singularity formation in the Yang-Mills flow”, Calc. Var. Partial Differential Equations, 19(2):211–220

    更新日期:2019-08-31
  • Nonlinear stability results for the modified Mullins–Sekerka and the surface diffusion flow
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-08-31
    E. Acerbi; N. Fusco; V. Julin; M. Morini

    It is shown that any three-dimensional periodic configuration that is strictly stable for the area functional is exponentially stable for the surface diffusion flow and for the Mullins–Sekerka or Hele–Shaw flow. The same result holds for three-dimensional periodic configurations that are strictly stable with respect to the sharp-interface Ohta–Kawaski energy. In this case, they are exponentially stable

    更新日期:2019-08-31
  • Genus bounds for min-max minimal surfaces
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-07-16
    Daniel Ketover

    We prove optimal genus bounds for minimal surfaces arising from the min-max construction of Simon–Smith. This confirms a conjecture made by Pitts–Rubinstein in 1986.

    更新日期:2019-07-16
  • Lorentzian Einstein metrics with prescribed conformal infinity
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-07-16
    Alberto Enciso; Niky Kamran

    We prove a local well-posedness theorem for the $(n+1)$-dimensional Einstein equations in Lorentzian signature, with initial data $(\widetilde{g},K)$ whose asymptotic geometry at infinity is similar to that anti-de Sitter (AdS) space, and compatible boundary data $\widehat{g}$ prescribed at the time-like conformal boundary of space-time. More precisely, we consider an $n$-dimensional asymptotically

    更新日期:2019-07-16
  • Quantitative flatness results and $BV$-estimates for stable nonlocal minimal surfaces
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-07-16
    Eleonora Cinti; Joaquim Serra; Enrico Valdinoci

    We establish quantitative properties of minimizers and stable sets for nonlocal interaction functionals, including the $s$-fractional perimeter as a particular case. On the one hand, we establish universal $BV$-estimates in every dimension $n \geqslant 2$ for stable sets. Namely, we prove that any stable set in $B_1$ has finite classical perimeter in $B_{1/2}$, with a universal bound. This nonlocal

    更新日期:2019-07-16
  • Min-max embedded geodesic lines in asymptotically conical surfaces
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-07-16
    Alessandro Carlotto; Camillo De Lellis

    We employ min-max methods to construct uncountably many, geometrically distinct, properly embedded geodesic lines in any asymptotically conical surface of non-negative scalar curvature, a setting where minimization schemes are doomed to fail. Our construction provides control of the Morse index of the geodesic lines we produce, which will be always less or equal than one (with equality under suitable

    更新日期:2019-07-16
  • Dehn filling and the Thurston norm
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-07-16
    Kenneth L. Baker; Scott A. Taylor

    For a compact, orientable, irreducible $3$-manifold with toroidal boundary that is not the product of a torus and an interval or a cable space, each boundary torus has a finite set of slopes such that, if avoided, the Thurston norm of a Dehn filling behaves predictably. More precisely, for all but finitely many slopes, the Thurston norm of a class in the second homology of the filled manifold plus

    更新日期:2019-07-16
  • Sharp fundamental gap estimate on convex domains of sphere
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-06-06
    Shoo Seto; Lili Wang; Guofang Wei

    In their celebrated work, B. Andrews and J. Clutterbuck proved the fundamental gap (the difference between the first two eigenvalues) conjecture for convex domains in the Euclidean space [3] and conjectured similar results hold for spaces with constant sectional curvature. We prove the conjecture for the sphere. Namely when $D$, the diameter of a convex domain in the unit $\mathbb{S}^n$ sphere, is

    更新日期:2019-06-06
  • Rigidity of pairs of rational homogeneous spaces of Picard number $1$ and analytic continuation of geometric substructures on uniruled projective manifolds
    J. Differ. Geom. (IF 2.167) Pub Date : 2019-06-06
    Ngaiming Mok; Yunxin Zhang

    Building on the geometric theory of uniruled projective manifolds by Hwang–Mok, which relies on the study of varieties of minimal rational tangents (VMRTs) from both the algebro-geometric and the differential-geometric perspectives, Mok, Hong–Mok and Hong–Park have studied standard embeddings between rational homogeneous spaces $X = G/P$ of Picard number $1$. Denoting by $S \subset X$ an arbitrary

    更新日期:2019-06-06
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