math.DG papers | Gist.Science

On the rigidity of special and exceptional geometries with torsion a closed $3$-form

This paper establishes that Riemannian manifolds admitting a connection with closed, covariantly constant torsion decompose locally into a product of a semisimple Lie group and a torsion-free manifold, a result used to simplify proofs for special geometries like KT and HKT manifolds and to fully characterize the geometry of complete, simply connected $G_2$ , $\mathrm{Spin}(7)$ , and compact 8-dimensional HKT manifolds under these conditions.

Georgios PapadopoulosTue, 10 Ma🔢 math

Hölder Regularity of Dirichlet Problem For The Complex Monge-Ampère Equation

This paper establishes the global Hölder continuity of solutions to the Dirichlet problem for the complex Monge-Ampère equation on strictly pseudoconvex domains or Hermitian manifolds, assuming the right-hand side belongs to $L^p$ and the boundary data are Hölder continuous.

Yuxuan Hu, Bin ZhouTue, 10 Ma🔢 math

$\del\delbar$ -Lemma and Bott-Chern cohomology of twistor spaces

This paper investigates the Bott-Chern and Aeppli cohomologies of twistor spaces associated with compact self-dual 4-manifolds to characterize the validity of the $\partial\bar{\partial}$ -lemma, while explicitly computing the Dolbeault cohomology for the twistor space of the flat 4-torus as a specific example where the lemma fails.

Anna Fino, Gueo Grantcharov, Nicoletta Tardini, Adriano Tomassini, Luigi VezzoniTue, 10 Ma🔢 math

On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups

This paper constructs and classifies all differential symmetry breaking operators between principal series representations of the de Sitter and Lorentz groups $SO_0(4,1) \supset SO_0(3,1)$ , proving that all such operators are necessarily differential and constitute "sporadic" cases that cannot be derived from meromorphic families via residue formulas.

Víctor Pérez-ValdésTue, 10 Ma🔢 math

Ergodic and Entropic Behavior of the Harmonic Map Heat Flow to the Moduli Space of Flat Tori

This paper establishes that the harmonic map heat flow from a compact Riemannian manifold into the moduli space of unit-area flat tori is stable, ergodic, and converges to the normalized hyperbolic measure, with the relative entropy decaying to zero to quantify this information-theoretic equilibrium.

Mohammad Javad Habibi Vosta KolaeiTue, 10 Ma🔢 math

The holonomy Lie $\infty$ -groupoid of a singular foliation I

This paper constructs a finite-dimensional Kan simplicial manifold that integrates the universal Lie $\infty$ -algebroid of a singular foliation admitting a geometric resolution, utilizing a recursive application of bi-submersions to generalize the Androulidakis-Skandalis holonomy groupoid to a higher Lie groupoid setting.

Camille Laurent-Gengoux (IECL), Ruben Louis (UIUC)Tue, 10 Ma🔢 math

On the $\mathcal{D}^+_J$ operator on higher-dimensional almost Kähler manifolds

This paper introduces the $\mathcal{D}^+_J$ operator on higher-dimensional almost Kähler manifolds to investigate the $\bar{\partial}$ -problem and establish uniqueness and local existence results for a generalized Monge-Ampère equation, ultimately providing an elliptic system for the operator and reorganizing the work of Tosatti-Weinkove-Yau.

Qiang Tan, Hongyu Wang, Ken Wang, Zuyi ZhangTue, 10 Ma🔢 math

Non-Shrinking Ricci Solitons of cohomogeneity one from the quaternionic Hopf fibration

This paper establishes the existence of non-Einstein, non-shrinking Ricci solitons on $\mathbb{H}^{m+1}$ , $\mathbb{HP}^{m+1}\backslash\{*\}$ , and $\mathbb{O}^2$ , including specific subfamilies of asymptotically paraboloidal steady solitons derived from the quaternionic Hopf fibration and related geometric structures.

Hanci ChiTue, 10 Ma🔢 math

Geometric scattering for nonlinear wave equations on the Schwarzschild metric

This paper establishes a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime by combining energy decay estimates with Sobolev embeddings to construct a bounded, locally Lipschitz scattering operator that maps past to future scattering data.

Pham Truong XuanTue, 10 Ma🔢 math

Rigidity of spin fill-ins with non-negative scalar curvature

This paper establishes new mean curvature rigidity theorems for spin fill-ins with non-negative scalar curvature by employing two distinct spinorial techniques—an APS boundary value problem extension and an index-theoretic comparison—to resolve questions posed by Miao and Gromov, while also deriving a novel Witten-type mass inequality for asymptotically Schwarzschild manifolds.

Simone Cecchini, Sven Hirsch, Rudolf ZeidlerTue, 10 Ma🔢 math

A gluing construction of singular solutions for a fully non-linear equation in conformal geometry

This paper demonstrates that the classical Mazzeo-Pacard gluing method can be successfully extended to construct singular solutions for the fully non-linear $\sigma_2$ -Yamabe equation in dimensions $n>4$ , provided the singular set consists of disjoint closed submanifolds with dimensions strictly less than $(n-\sqrt{n}-2)/2$ .

María Fernanda Espinal, María del Mar GonzálezTue, 10 Ma🔢 math

An index bound for smooth umbilic points

This paper proves that the local index of an isolated umbilic point on a $C^{3+\alpha}$ -smooth convex surface in Euclidean 3-space is strictly less than two by employing a "totally real blow-up" technique to reduce the local problem to a global result regarding Lagrangian surfaces, thereby suggesting the potential existence of exotic umbilic points with index 3/2 that exceed the bounds known for real analytic surfaces.

Brendan Guilfoyle, Wilhelm KlingenbergTue, 10 Ma🔢 math

The Kerr-Newman two-twistor particle

This paper presents an all-orders worldline effective action for Kerr-Newman black holes within twistor particle theory and identifies exact hidden symmetries in self-dual backgrounds.

Joon-Hwi KimTue, 10 Ma🔢 math

Mass and rigidity in almost Kähler geometry

This paper establishes an explicit formula for the ADM mass of asymptotically locally Euclidean almost Kähler manifolds using a spin $^\mathbb{C}$ adaptation of Witten's proof, and subsequently derives positive mass theorems, Penrose-type inequalities, and rigidity results showing that certain almost Kähler-Einstein manifolds are necessarily Kähler-Einstein.

Partha GhoshTue, 10 Ma🔢 math

Instanton construction of the mapping cone Thom-Smale complex

This paper constructs an instanton cochain complex using the eigenspaces of a deformed mapping cone Laplacian and proves its cochain isomorphism to the topologically defined mapping cone Thom-Smale complex, thereby establishing a bridge between analytic and topological approaches to the wedge by a smooth closed form.

Hao ZhuangTue, 10 Ma🔢 math

Flexibility of Codimension One $C^{1,\theta}$ Isometric Immersions

This paper improves the known threshold for the flexibility of $C^{1,\theta}$ isometric immersions of $n$ -dimensional Riemannian metrics into $\mathbb{R}^{n+1}$ by proving that any short immersion can be approximated by such immersions for $\theta < 1/(1+2(n-1))$ when $n \geq 3$ , utilizing a refined convex integration scheme with enhanced iterative integration by parts.

Dominik InauenTue, 10 Ma🔢 math

Barta Theorem for the $p$ -Laplacian and Geometric Applications

This paper establishes a Barta-type formulation for the $p$ -Laplacian on Riemannian manifolds to derive sharp lower bounds for the $p$ -fundamental tone without boundary regularity assumptions, leading to nonlinear extensions of classical spectral comparison theorems and geometric characterizations for minimal immersions.

Paulo Henryque C. SilvaTue, 10 Ma🔢 math

Horizontal curvatures of surfaces in 3D contact sub-Riemannian Lie groups

This paper employs a Riemannian approximation scheme to derive explicit formulas for horizontal curvatures and symplectic distortion of surfaces in 3D contact sub-Riemannian Lie groups, specifically classifying surfaces of revolution with constant curvatures in the Heisenberg and affine-additive groups.

Elia Bubani, Andrea Pinamonti, Ioannis D. Platis, Dimitrios TsolisTue, 10 Ma🔢 math

Fat Lie Theory

This paper introduces the framework of "fat Lie theory" to establish a one-to-one correspondence between fat extensions and abstract 2-term representations up to homotopy, while demonstrating that fat extensions of groupoids correspond to general linear PB-groupoids and core extensions to vertically/horizontally core-transitive double groupoids, thereby upgrading existing correspondences to equivalences of categories.

Lennart ObsterTue, 10 Ma🔢 math

A reverse isoperimetric inequality in three-dimensional space forms

This paper proves a sharp reverse isoperimetric inequality in three-dimensional space forms of constant curvature, demonstrating that among all $\lambda$ -convex bodies with a fixed surface area, the $\lambda$ -convex lens uniquely minimizes volume, thereby confirming Borisenko's Conjecture for non-zero curvature cases.

Kostiantyn Drach, Gil Solanes, Kateryna TatarkoTue, 10 Ma🔢 math

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