arXiv research

Characterizes Kähler-hyperbolicity of bounded symmetric domains based on rank and genus.

Characterizes visibility and geodesic loops in complex domains.

Study shows how many domains are needed for generalization, using a new measure called domain shattering dimension.

The paper proves Gromov hyperbolicity of certain metrics using isoperimetric inequalities.

Sheng and Zuo's characteristic forms are invariants of a variation of Hodge structure. We show that they characterize Gross's canonical variations of Hodge structure of Calabi-Yau type over (Hermitian symmetric) tube domains.

In this paper we study the area of ideals triangles in a convex domain with its Hilbert geometry. We obtain a characterization of the hyperbolic geometry among all the Hilbert geometry in terms of area of ideals triangles. We also obtain a sharp lower bound on the hilbert area of ideal triangles, independant of the con…

Extends Polydisk Theorem to Cartan-Hartogs domains.

Characterizes billiard and quasigeodesic flows in polyhedral convex bodies.

We consider the Johnson-Koranyi-Hua system on symmetric Siegel domains of type two. We prove that all functions which are annihilated by the system and satisfy an H^2 integrability condition are pluriharmonic. So the situation is completely different on type two domains than on tube type domains: it was proved by Johns…

Adversarial techniques learn invariant representations across multiple domains.

In this paper we prove: if the complete Kähler-Einstein metric on a bounded convex domain (with no boundary regularity assumptions) is Gromov hyperbolic, then the $\bar{\partial}$-Neumann problem satisfies a subelliptic estimate. This is accomplished by constructing bounded plurisubharmonic function whose Hessian grows…

Paper finds inequalities for convex domains in hyperbolic space.

Method approximates Lipschitz domains with smoother shapes.

Study on regularity of optimal transport maps on convex domains with quadratic cost.

We obtain sharp lower bounds on the radii of inscribed balls for strictly convex isoperimetric domains lying in a 2-dimensional Alexandrov metric space of curvature bounded below. We also characterize the case when such bounds are attained.

We give two characterizations of varieties whose universal cover is a bounded symmetric domain without ball factors in terms of the existence of a holomorphic endomorphism \s of the tensor product T\otimes T' of the tangent bundle T with the cotangent bundle T'. To such a curvature type tensor \s one associates the fir…

Uniformizes klt pairs using bounded symmetric domains.

For a domain $Ω\subset\mathbb R^n$, we introduce the concept of a uniformly $C^m$ defining function. We characterize uniformly $C^m$ defining functions in terms of the signed distance function for the boundary and provide a large class of examples of unbounded domains with uniformly $C^m$ defining functions. Some of ou…

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the $\MIT$ bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.

In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the automorphism group and the regularity of the boundary.

We review some recent results in the generic rigidity theory of planar frameworks with forced symmetry, giving a uniform treatment to the topic. We also give new combinatorial characterizations of minimally rigid periodic frameworks with fixed-area fundamental domain and fixed-angle fundamental domain.

Study Anosov representations of reducible suspensions of hyperbolic groups.

This paper establishes a theoretical foundation for super-models via domain adaptation.

Characterizes kernel of linearization for minimal surfaces problem

In 1929, Paul Funk and Ludwig Berwald gave a characterization of Hilbert geometries from the Finslerian viewpoint. They showed that a smooth Finsler metric in a convex bounded domain of $\mathbb{R}^n$ is the Hilbert geometry in that domain if and only if it is complete, if its geodesics are straight lines and if its fl…

The Wong-Rosay theorem characterizes the strongly pseudoconvex domains of $\mathbb{C}^n$ by their automorphism groups. It has a lot of generalizations to other kinds of domains (for example, the weakly pseudoconvex domains). However, most of them are for domains of $\mathbb{C}^n$. In this note, we generalize the Wong-R…

Sequential data often originates from diverse domains across which statistical regularities and domain specifics exist. To specifically learn cross-domain sequence representations, we introduce disentangled state space models (DSSM) -- a class of SSM in which domain-invariant state dynamics is explicitly disentangled f…

Sharp estimates for heat flow on nonconvex domains.

Researchers identify valid auxiliary functions for extreme value distributions and their max-domains of attraction.

Valid certifies LLMs' domain adherence, bounding out-of-domain behavior.

We study how the existence of a negatively pinched Kähler metric on a domain in complex Euclidean space restricts the geometry of its boundary. In particular, we show that if a convex domain admits a complete Kähler metric, with pinched negative holomorphic bisectional curvature outside a compact set, then the boundary…

In constant curvatures spaces, there are a lot of characterizations of geodesic balls as optimal domain for shape optimization problems. Although it is natural to expect similar characterizations in rank one symmetric spaces, very few is known in this setting. In this paper we prove that, in a non-compact rank one symm…

The paper characterizes gauge balls in the Heisenberg group and solves overdetermined problems.

This paper is devoted to the study of convergence of sequences of solutions to the constant mean curvature H equation. The convergence domain is defined. The main Theorem characterizes the complement of this convergence domain: it shows that circle arcs of curvature 2H compose this complement. We then give results whic…

Sharp estimates for Finsler metrics in convex domains.

We provide monotonicity formulas for solutions to the p-Laplace equation defined in the exterior of a convex domain. A number of analytic and geometric consequences are derived, including the classical Minkowski inequality as well as new characterizations of rotationally symmetric solutions and domains. The proofs rely…

In the current article our primary objects of study are compact complex submanifolds of quotient manifolds of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms. We are interested in the characterization of the totally geodesic submanifolds among compact splitting complex submanifo…

The paper resolves a problem about metric inequivalence and characterizes proper holomorphic maps.

We prove that in Riemannian manifolds the $k$-th Steklov eigenvalue on a domain and the square root of the $k$-th Laplacian eigenvalue on its boundary can be mutually controlled in terms of the maximum principal curvature of the boundary under sectional curvature conditions. As an application, we derive a Weyl-type upp…

Extends Carathéodory's theorem to multidimensional domains with constant curvature.

The paper improves classification accuracy by leveraging a shared signal across domains in high-dimensional classification.

Adversarial weighting improves regression task adaptation.

Domain adaptation addresses the common problem when the target distribution generating our test data drifts from the source (training) distribution. While absent assumptions, domain adaptation is impossible, strict conditions, e.g. covariate or label shift, enable principled algorithms. Recently-proposed domain-adversa…

Convex domains have a unique boundary property related to normal vectors.

Solves complex Monge-Ampère equation for measures with pluripolar parts.

Symplectic homology matches dual capacities for convex domains.

A characterization of maximal domains of existence of adapted complex structures for Riemannian homogeneous manifolds under certain extensibility assumptions on their geodesic flow is given. This is applied to generalized Heisenberg groups and naturally reductive Riemannian homogeneous spaces. As an application it is s…

Novel unsupervised scheme for highly imbalanced and overlapping datasets.