A Lower Bound of the First Eigenvalue of a Closed Manifold with Negative Lower Bound of the Ricci Curvature

2004/06/28 by Jun Ling, Ling, Jun
Mathematics · #35P15 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Primary 58J50 #Secondary 53C21 #math.AP #math.DG #msc:35P15 #msc:53C21 #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0406562

Title changed

openalex publication_date 2004/06/28 · arxiv created 2004/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Along the line of the Yang Conjecture, we give a new estimate on the lower bound of the first non-zero eigenvalue of a closed Riemannian manifold with negative lower bound of Ricci curvature in terms of the in-diameter and the lower bound of Ricci curvature.

Related

• A Lower Bound of The First Eigenvalue of a Closed Manifold with Positive Ricci Curvature
• The first Dirichlet Eigenvalue of a Compact Manifold and the Yang Conjecture
• Lower Bounds of the First Closed and Neumann Eigenvalues of Compact Manifolds with Positive Ricci Curvature
• A Lower Bound of the First Dirichlet Eigenvalue of a Compact Manifold with Positive Ricci Curvature
• Lower bounds for the first eigenvalue of the Laplacian on K "ahler\n manifolds