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
收藏
页码：227 / 234
页数：8
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