A LOWER BOUND OF THE FIRST DIRICHLET EIGENVALUE OF A COMPACT MANIFOLD WITH POSITIVE RICCI CURVATURE

DOI10.1142/S0129167X06003631zbMath1116.58029arXivmath/0406120MaRDI QIDQ5483425

Jun Ling

Publication date: 14 August 2006

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406120

zbMATH Keywords

maximum principleeigenvaluelower boundLaplace Beltrami operatorinterior radiusnonnegative mean curvatureRicci positive

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (4)

Lower bounds of the eigenvalues of compact manifolds with positive Ricci curvature ⋮ A lower bound for the first eigenvalue in the Laplacian operator on compact Riemannian manifolds ⋮ Lower estimates for the first eigenvalue of the Laplace operator on doubly connected domains in a Riemannian manifold ⋮ Uncertainty principle on 3-dimensional manifolds of constant curvature

Cites Work

• On the Schrödinger equation and the eigenvalue problem
• Lower bound estimates of the first eigenvalue for compact manifolds with positive Ricci curvature
• Variational formulas and approximation theorems for the first eigenvalue in dimension one
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