相关论文: Bipolar comparison
Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, and assume that X is defined over a function field admitting K as a completion. Let further m be a positive measure on X…
In this paper I present a comparison theorem for the waist of Riemannian manifolds with positive sectional curvature. The main theorem of this paper gives a partial positive answer to a conjecture formulated by M.Gromov in [8]. The content…
We prove a version of Topogonov's triangle comparison theorem with surfaces of revolution as model spaces. Given a model surface and a Riemannian manifold with a fixed base point, we give necessary and sufficient conditions under which…
We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equations and a corresponding modified Benamou-Brenier formula.…
We shall present a measure theoretical approach for which together with the Kantorovich duality provide an efficient tool to study the optimal transport problem. Specifically, we study the support of optimal plans where the cost function…
The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-R\"ollin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The more general linear regression condition…
In this paper we provide a new method for establishing the rotational symmetry of the solutions to a couple of very classical overdetermined problems arising in potential theory, in both the exterior and the interior punctured domain.…
The Bradley-Terry-Luce (BTL) model is a benchmark model for pairwise comparisons between individuals. Despite recent progress on the first-order asymptotics of several popular procedures, the understanding of uncertainty quantification in…
Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n \geq 2$. This paper concerns to the validity of the optimal Riemannian $L^1$-Entropy inequality \[ {\bf Ent}_{dv_g}(u) \leq n \log \left(A_{opt} \|D u\|_{BV(M)} +…
The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing…
Let Riemannian metrics $g$ and $\bar g$ on a connected manifold $M^n$ have the same geodesics (considered as unparameterized curves). Suppose the eigenvalues of one metric with respect to the other are all different at a point. Then, by the…
We introduce a definition of pressure for almost-additive sequences of continuous functions defined over (non-compact) countable Markov shifts. The variational principle is proved. Under certain assumptions we prove the existence of Gibbs…
In a recent and ongoing work, Baldwin and Klemperer explored a connection between tropical geometry and economics. They gave a sufficient condition for the existence of competitive equilibrium in product-mix auctions of indivisible goods.…
It is known that noncommutative Yang-Mills theory with periodical boundary conditions on torus at the rational value of the noncommutativity parameter is Morita equivalent to the ordinary Yang-Mills theory with twisted boundary conditions…
Let (X,L) be a (semi-) polarized complex projective variety and T a real torus acting holomorphically on X with moment polytope P. Given a probability density g on P we introduce a new type of Monge-Ampere measure on X, defined for singular…
In this paper, we investigate the existence and uniqueness of fixed points for self-mappings defined on bipolar metric spaces using a new class of contractive conditions, namely polynomial-type contractions. Our main results establish…
Building on the recent work of Mushaandja and Olela-Otafudu~\cite{MushaandjaOlela2025} on modular metric topologies, this paper investigates extended structural properties of modular (pseudo)metric spaces. We provide necessary and…
We consider an abundant class of non-uniformly hyperbolic $C^2$-H\'enon like diffeomorphisms called strongly regular and which corresponds to Benedicks-Carleson parameters. We prove the existence of $m>0$ such that for any such…
In this paper, we extend the sharp lower bounds of spectal gap, due to Chen- Wang [10, 11], Bakry-Qian [6] and Andrews-Clutterbuck [5], from smooth Riemaniannian manifolds to general metric measure spaces with Riemannian curvature-dimension…
Akemann and Weaver showed Lyapunov-type theorem for rank one positive semidefinite matrices which is an extension of Weaver's KS$_2$ conjecture that was proven by Marcus, Spielman, and Srivastava in their breakthrough solution of the…