arXiv research

Uniform estimates for elliptic problems near polygonal domains.

The paper studies invariant weighted Bergman metrics on domains.

Uniformizes klt pairs using bounded symmetric domains.

Equivalence proven between uniformizing varieties and tensors, generalizing uniformization results.

Uniform convexity in divisible domains leads to hyperbolic geometry.

Graph-Relational Domain Adaptation (GRDA) adapts domains based on their graph structure.

We show here that the Nielsen core of the bumping set of the domain of discontinuity of a Kleinian group $Γ$ is the boundary of the characteristic submanifold of the associated 3-manifold with boundary. Some examples of interesting characteristic submanifolds are given. We also give a construction of the characteristic…

The paper proposes a uniformity regularization scheme to improve deep neural network transferability.

New approach to extremal hyperbolic surfaces using NEC groups.

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as starting point the spherical CR uniformization of the Whitehead link complement constructed by Parker and Will, using a Ford domain in the co…

Defines W-volume for planar domains with circular boundaries, relating to Laplacian determinant and Schottky uniformization.

The paper studies complex Finsler metrics and their equivalence to the Kobayashi metric.

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.

We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remains parabolic) also give a uniformization of the figure eight knot comp…

Period maps surjective for certain gravitational instantons.

Method approximates Lipschitz domains with smoother shapes.

Uniformizes compact complex manifolds via Anosov representations.

New uniformity tester ensures consistent results across different samples.

New approach to adversarial robustness with non-uniform perturbations.

A geometric framework for metrics of maximal acceleration which is applicable to large proper accelerations is discussed, including a theory of connections associated with the geometry of maximal acceleration. In such a framework it is shown that the uniform bound on the proper maximal acceleration implies an uniform b…

Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain dimension $n$, we show a uniform $C^{1,α}$-regularity result for a sequence of such …

The current article stems from our study on the asymptotic behavior of holomorphic isometric embeddings of the Poincaré disk into bounded symmetric domains. As a first result we prove that any holomorphic curve exiting the boundary of a bounded symmetric domain $Ω$ must necessarily be asymptotically totally geodesic. A…

Extends Langevin dynamics for constrained domains.

New subsets without interior support Poincaré inequalities, expanding previous results.

This work establishes uniform convergence of subdifferentials in stochastic optimization.

Uniformizes Hodge structures, proving Lyapunov exponents and log-Anosov monodromy.

We show that the nearest point retraction is a uniform quasi-isometry from the Thurston metric on a hyperbolic domain in the Riemann sphere to the boundary of the convex hull of its complement. As a corollary, one obtains explicit bounds on the quasi-isometry constant of the nearest point retraction with respect to the…

There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example, over a domain of size $n$, distinguishing the uniform distribution from distrib…

Sharp stability of isometries on Heisenberg group proven.

This study uses neural networks to approximate Bayesian filtering problems.

Unified method to calculate Gromov norm for Kähler classes of bounded symmetric domains.

We prove that if $D\subset C^n$ is a bounded domain with real analytic boundary and D is pseudoconvex then the compact open topology in the group of holomorphic automorphisms of D is the topology of uniform convergence on D.

Minimum width for ReLU networks on compact domain is exactly max{d_x, d_y, 2}

Algorithm adapts to shifting domains with minimal label queries.

One fundamental goal in any learning algorithm is to mitigate its risk for overfitting. Mathematically, this requires that the learning algorithm enjoys a small generalization risk, which is defined either in expectation or in probability. Both types of generalization are commonly used in the literature. For instance, …

We extend our discrete uniformization theorems for planar, $m$-connected, Jordan domains [Journal für die reine und angewandte Mathematik 670 (2012), 65--92] to closed surfaces of non-positive genus.

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on thes…

In recent work, we have proven uniform decay bounds for solutions of the wave equation $\Box_gφ=0$ on a Schwarzschild exterior, in particular, the uniform pointwise estimate $|φ|\le Cv_+^{-1}$, which holds throughout the domain of outer communications, where $v$ is an advanced Eddington-Finkelstein coordinate, $v_+=\ma…

Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain adaptation. We propose AlignFlow, a generative modeling framework that models each dom…

In this paper we study the automorphism group of smoothly bounded convex domains. We show that such a domain is biholomorphic to a "polynomial ellipsoid" (that is, a domain defined by a weighted homogeneous balanced polynomial) if and only if the limit set of the automorphism group intersects at least two closed comple…

Let $(M^n, g)$ be a complete non-compact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. We prove that $M$ is holomorphically covered by a pseudoconvex domain in $\C^n$ which is homeomorphic to $\R^{2n}$, provided $(M^n, g)$ has uniform linear average quadratic curvature decay.

Uniform convergence of metrics on surfaces with bounded curvature measures proved.

We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauss curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In particular, for bounded domains we prove that convex functions with prescribed …

Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit …

The paper develops quantitative estimates for holomorphic sections over bounded domains.

Paper tackles estimating initial conditions of spatio-temporal processes from sparse data.

A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition and Poisson's equation with mixed boundary conditions. The principal advantage o…