• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• J. Differ. Geom. (IF 2.167) Pub Date : 2020-09-05

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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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