Uniqueness of Conformal Metrics with Constant Q-Curvature on Closed Einstein Manifolds

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2023-12-18 DOI:10.1007/s11118-023-10117-1

Jérôme Vétois

引用次数: 0

Abstract

On a smooth, closed Einstein manifold (M, g) of dimension \(n \ge 3\) with positive scalar curvature and not conformally diffeomorphic to the standard sphere, we prove that the only conformal metrics to g with constant Q-curvature of order 4 are the metrics \(\lambda \) g with \(\lambda > 0\) constant.

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封闭爱因斯坦曲率恒定的共形度量的唯一性

在具有正标量曲率且不与标准球面保角衍射的光滑闭合爱因斯坦流形（M, g）上，我们证明了唯一具有4阶恒定Q曲率的g的保角度量是具有恒定Q曲率的度量（（\lambda \）g）。

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.