A sharp lower bound for the first eigenvalue on Finsler manifolds with nonnegative weighted Ricci curvature. (April 2015)

• Record Type: Journal Article
• Authors: Xia, Qiaoling
• Is Part Of: Nonlinear analysis. Volume 117(2015)
• Page Start: 189
• Page End: 199
• Publication Date: 2015-04
• Subjects: 53C60 -- 35P15; Finsler Laplacian -- First eigenvalue -- Weighted Ricci curvature -- Convex boundary; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.01.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let ( M, F ) be an n -dimensional compact Finsler manifold without boundary or with a convex boundary and λ 1 be the first (nonzero) closed or Neumann eigenvalue of the Finsler Laplacian on M with nonnegative weighted Ricci curvature. In this paper, we prove that λ 1 ≥ π 2 d 2, where d is the diameter of M, and that the equality holds if and only if M is a 1 -dimensional circle or a 1 -dimensional segment, which generalize the well-known Zhong–Yang's sharp estimate in Riemannian geometry (Zhong and Yang, 1984).