Lower Bound for the Green Energy of Point Configurations in Harmonic Manifolds

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2023-10-19 DOI:10.1007/s11118-023-10108-2

Carlos Beltrán, Víctor de la Torre, Fátima Lizarte

引用次数: 0

Abstract

Abstract In this paper, we get the sharpest known to date lower bounds for the minimal Green energy of the compact harmonic manifolds of any dimension. Our proof generalizes previous ad-hoc arguments for the most basic harmonic manifold, i.e. the sphere, extending it to the general case and remarkably simplifying both the conceptual approach and the computations.

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调和流形中点构型绿色能量的下界

摘要本文得到了任意维紧化调和流形的最小Green能量的已知最尖锐下界。我们的证明推广了之前关于最基本的调和流形(即球面)的特别论证，将其推广到一般情况，并显著地简化了概念方法和计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.