arXiv research

Study examines maximal domains of radial harmonic functions across different curvature types.

The study classifies area-maximizing hypersurfaces with singularities and exterior domains.

Proves local maximizers for higher Ekeland-Hofer capacities in 4D star-shaped domains.

Proposes MEDM to balance entropy minimization and diversity maximization for better domain adaptation.

The ball maximizes the first biharmonic Steklov eigenvalue.

Maximal spacetimes have unique past/future sets.

Study exterior maximal surfaces with precise asymptotic behavior.

Maximal surfaces in Lorentz-Minkowski space have conjugate graphs.

In this paper we study the maximal stable domains on minimal catenoids in Euclidean and hyperbolic spaces and in $H^2 \times R$. We in particular investigate whether half-vertical catenoids are maximal stable domains (\emph{Lindelöf's property}). We also consider stable domains on catenoid-cousins in hyperbolic space. …

InfoOT improves data alignment by maximizing mutual information.

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…

Anosov representations lead to compact domains in flag manifolds.

MDA learns domain-invariant features for better target domain classification.

Maximal solution of a PDE shows boundary smoothness for certain domains.

Maximal acceleration metrics limit spacetime curvature.

In this paper, we study the Dirichlet problem associated to the maximal surface equation. We prove the uniqueness of bounded solutions to this problem in unbounded domain in R^2.

Given a smooth simply connected planar domain, the area is bounded away from zero in terms of the maximal curvature alone. We show that in higher dimensions this is not true, and for a given maximal mean curvature we provide smooth embeddings of the ball with arbitrary small volume.

The paper studies continuous submodular functions and their optimization.

This paper addresses classification tasks on a particular target domain in which labeled training data are only available from source domains different from (but related to) the target. Two closely related frameworks, domain adaptation and domain generalization, are concerned with such tasks, where the only difference …

A totally geodesic map $f:\mathcal X_1\to\mathcal X_2$ between Hermitian symmetric spaces is tight if its image contains geodesic triangles of maximal area. Tight maps were first introduced in [BIW09], and were classified in [Ham13, Ham14, HO14] in the case of irreducible domain. We complete the classification by analy…

Paper introduces a new Poisson kernel for strongly pseudoconvex domains.

Two geodesic balls maximize the third Neumann eigenvalue in hyperbolic space.

ImplicitCE recommends items to new users by co-embedding users and items.

Paper finds space-like maximal surfaces with entire null lines in 3D space-time.

Paper proves isoperimetric inequality for Minkowski spacetime.

Anchor PCA improves robustness in multi-domain PCA.

Study Bergman metric on Cartan-Hartogs domains and their duals.

A method to improve image synthesis diversity using mutual information.

We describe a construction of Schottky type subgroups of automorphism groups of partially cyclically ordered sets. We apply this construction to the Shilov boundary of a Hermitian symmetric space and show that in this setting Schottky subgroups correspond to maximal representations of fundamental groups of surfaces wit…

If the Lorentzian norm on a maximal surface in the 3-dimensional Lorentz-Minkowski space $R_1^3$ is positive and proper, then the surface is relative parabolic. As a consequence, entire maximal graphs with a closed set of isolated singularities are relative parabolic. Furthermore, maximal and minimal graphs over closed…

The paper examines Euclidean domains with nearly maximal Yamabe quotients.

Paper tackles domain generalization by minimizing domain-based covariance.

We define a family of four-point invariants for Shilov boundaries of bounded symmetric domains of tube type, which generalizes the classical four-point cross ratio on the unit circle. This generalization, which is based on a similar construction of Clerc and Ørsted, is functorial and well-behaved under products; these …

We study the canonical complexifications of non-compact Riemannian symmetric spaces G/K by the Grauert tube construction. We determine the maximal such complexification, a domain already constructed in another context by Akhiezer and Gindikin (Math. Ann., 1990), and show that this domain is Stein. We show there is an a…

We obtain the Weierstrass-Enneper representation for maximal graphs(whose Gauss map is one-one) in Lorentz-Minkowski space. For this we use the method of Barbishov and Chernikov, which they have used to find the solutions of Born-Infeld equation in hodographic coordinates. We could use their method in our case, because…

TIM maximizes mutual information for few-shot learning, outperforming state-of-the-art methods.

SALT combines geometric and model-based alignment for domain adaptation.

A new method for unsupervised domain adaptation using Gaussian processes.

We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous fa…

We show that the ball does not maximize the first nonzero Steklov eigenvalue among all contractible domains of fixed boundary volume in $\mathbb{R}^n$ when $n \geq 3$. This is in contrast to the situation when $n=2$, where a result of Weinstock from 1954 shows that the disk uniquely maximizes the first Steklov eigenval…

Paper tackles cold-start domain adaptation with language descriptions.

In Euclidean and Hyperbolic space, and the hemisphere in $S^n$, geodesic balls maximize the gap $λ_2 - λ_1$ of Dirichlet eigenvalues, amoung domains with fixed $λ_1$. We prove an upper bound on $λ_2 - λ_1$ for domains in manifolds with certain curvature bounds. The inequality is sharp on geodesic balls in spaceforms.

Study sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces.

Learning multiple tasks across heterogeneous domains is a challenging problem since the feature space may not be the same for different tasks. We assume the data in multiple tasks are generated from a latent common domain via sparse domain transforms and propose a latent probit model (LPM) to jointly learn the domain t…

In this paper, it is shown that a Fuchsian group, acting on the upper half-plane model for $\mathbb{H}^2$, admits a Ford domain which is also a Dirichlet domain, for some center, if and only if it is an index 2 subgroup of a reflection group. This is used to exhibit an example of a maximal arithmetic hyperbolic reflect…

Domain adaptation (DA) is the task of classifying an unlabeled dataset (target) using a labeled dataset (source) from a related domain. The majority of successful DA methods try to directly match the distributions of the source and target data by transforming the feature space. Despite their success, state of the art m…

This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend previous descriptions of the dual domain then exploit the link between the constra…

In this paper we prove that given a volume, among all domains with smooth boundary in rank-1 symmetric spaces of noncompact type, geodesic balls maximizes the first nonzero Steklov eigenvalue. We also prove a comparison result for the first nonzero Steklov eigenvalue for domains in simply connected Riemannian manifolds…