arXiv research

Geometric inequalities for static convex domains in hyperbolic space proved.

The study proves geometric inequalities for static convex domains in static rotationally symmetric spaces.

Paper finds inequalities for convex domains in hyperbolic space.

Paper proves inequalities in sub-static warped product manifolds.

In this article, we first establish the main tool - an integral formula for Riemannian manifolds with multiple boundary components (or without boundary). This formula generalizes Reilly's original formula from \cite{Re2} and the recent result from \cite{QX}. It provides a robust tool for sub-static manifolds regardless…

Paper defines Bartnik mass for hyperbolic extensions and proves staticity.

The paper studies static manifolds with boundary and their properties.

We propose to apply deep transfer learning from computer vision to static malware classification. In the transfer learning scheme, we borrow knowledge from natural images or objects and apply to the target domain of static malware detection. As a result, training time of deep neural networks is accelerated while high c…

We study the existence and uniqueness of solutions to the static vacuum Einstein equations in bounded domains, satisfying the Bartnik boundary conditions of prescribed metric and mean curvature on the boundary.

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Föllmer, Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the …

In this paper we extend the local scalar curvature rigidity result in [6] to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in general in the light of the paper [10]. We obtain the local scalar curvature rigidi…

The paper explores centroids and static equilibrium points in non-Euclidean geometries.

The paper proves a positive mass theorem for non-compact static domains in hyperbolic space.

The paper proves new inequalities for convex hypersurfaces in hyperbolic and spherical spaces.

We generalize Brendle's geometric inequality considered in \cite{B} to static manifolds. The inequality bounds the integral of inverse mean curvature of an embedded mean-convex hypersurface by geometric data of the horizon. As a consequence, we obtain a reverse Penrose inequality on static asymptotically locally hyperb…

Study on static manifolds with boundary and rigidity of curvature.

Neural networks can find financial arbitrage opportunities without needing market models.

We study solutions to the static vacuum Einstein equations on exterior domains with prescribed metric and mean curvature on the inner boundary. It is proved that for any such boundary data near the standard round boundary data in Euclidean space, there exists a unique AF solution to the static vacuum equations realizin…

We compute a Bochner type formula for static three-manifolds and deduce some applications in the case of positive scalar curvature. We also explain in details the known general construction of the (Riemannian) Einstein (n+1)-manifold associated to a maximal domain of a static n-manifold where the static potential is po…

We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand side data from some polynomially weighted Sobolev spaces and obtain solutions whi…

The paper tackles minimax optimality in continuum contextual bandits with Hölder continuity.

The paper solves three problems related to monostable polyhedra.

To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms have been successfully developed to minimize the adaptive regret. However, existi…

Optimal switching regret for all segmentations in online convex optimisation.

Recursive least-squares algorithms often use forgetting factors as a heuristic to adapt to non-stationary data streams. The first contribution of this paper rigorously characterizes the effect of forgetting factors for a class of online Newton algorithms. For exp-concave and strongly convex objectives, the algorithms a…

Classifies ancient convex curves in convex domains.

Study optimal semi-static hedging for illiquid markets using dynamic cash and static quoted derivatives.

Study classifies and characterizes translators in hyperbolic static universe.

New algorithm reduces constraint violation to $O(T^{1/3})$ while maintaining $O(\sqrt{T})$ regret.

The study shows how strictly convex domains in Euclidean spaces are rigid.

Reduces dynamic regret to static problem in RKHS.

Optimizes nonconvex optimization by converting it to static regret minimization.

Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorough and complete unde…

Symplectic homology matches dual capacities for convex domains.

Universal inequalities found for Laplacian eigenvalues on convex domains.

Universal inequalities for Laplacian eigenvalues on convex domains.

New inequalities for planar convex domains' Laplacian eigenvalues.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolicity of (non-smooth) domains.The results show the similarity of geometry of the bases of non-Gromov hyperbolic tube domains with the geometry …

Generalizes rigidity of scalar curvature for convex domains.

Solves equality case in isoperimetric inequality for non-convex domains.

Optimal inequality for free boundary hypersurfaces in convex domains.

Uniform convexity in divisible domains leads to hyperbolic geometry.

Fundamental gap vanishes for convex domains in hyperbolic space.

The paper examines hyperbolicity in bounded strongly minimally convex domains in R^d.

The Minkowski inequality is a classical inequality in differential geometry, giving a bound from below, on the total mean curvature of a convex surface in Euclidean space, in terms of its area. Recently there has been interest in proving versions of this inequality for manifolds other than R^n; for example, such an ine…

We give a necessary complex geometric condition for a bounded smooth convex domain in Cn, endowed with the Kobayashi distance, to be Gromov hyperbolic. More precisely, we prove that if a smooth bounded convex domain contains an analytic disk in its boundary, then the domain is not Gromov hyperbolic for the Kobayashi di…

In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the Grassmannian of $p$-planes in $\mathbb{R}^{2p}$ when $p > 1$. Moreover, this convex divisible domain is a model of the symmetric space associ…