A sharp lower bound for the first eigenvalue on Finsler manifolds with nonnegative weighted Ricci curvature

作者：Xia, Qiaoling^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2015, 117: 189-199.

DOI：10.1016/j.na.2015.01.018

• Finsler Laplacian
• First eigenvalue
• Weighted Ricci curvature
• Convex boundary

Let (M, F) be an n-dimensional compact Finsler manifold without boundary or with a convex boundary and lambda(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 lambda(1) >= pi(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).

• 出版日期2015-4
• 单位浙江大学