On a rigidity result for the first conformal eigenvalue of the Laplacian

被引：3

作者：

Petrides, Romain ^{[1
]}

机构：

[1] Univ Lyon 1, CNRS UMR 5208, Inst Camille Jordan, 43 Bd 11 Novembre 1918, F-69622 Villeurbanne, France

来源：

JOURNAL OF SPECTRAL THEORY | 2015年 / 5卷 / 01期

关键词：

Bounds; conformal; eigenvalue; Laplacian; conformal volume; Riemannian manifold; METRICS;

D O I：

10.4171/JST/95

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given (M, g) a smooth compact Riemannian manifold without boundary of dimension n >= 3, we consider the first conformal eigenvalue which is by definition the supremum of the first eigenvalue of the Laplacian among all metrics conformal to g of 2 volume 1. We prove that it is always greater than n omega(n/2)(n), the value it takes in the conformal class of the round sphere, except if (M, g) is conformally diffeomorphic to the standard sphere.

引用

页码：227 / 234

页数：8

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