Sharp spectral gap for the Finsler p-Laplacian

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（8）
• 页码范围: 1615-1644
• 页数: 30页
• 语种: 英文

摘要

In this paper,we give a sharp lower bound for the first (nonzero) p-eigenvalue on a compact Finsler manifold M without boundary or with convex boundary if the weighted Ricci curvature RicciN is bounded from below by a constant K in terms of the diameter d of a manifold,dimension,K,p and N.In particular,if RicciN is non-negative,then the first p-eigenvalue is bounded from below by (p-1)(πp/d)p,and the equality holds if and only if M is either a circle or a segment.