The sharp lower bound of the first Dirichlet eigenvalue for geodesic balls

DOI10.1007/s00209-021-02859-8zbMath1486.53053arXiv2108.06951OpenAlexW3198534108MaRDI QIDQ2069665

Yanyan Li

Publication date: 21 January 2022

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.06951

zbMATH Keywords

geodesic ballDirichlet eigenvalueuniform Poincaré inequality

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22)

Cites Work

• Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue
• \(L^ p\) and mean value properties of subharmonic functions on Riemannian manifolds
• Spectra of domains in compact manifolds
• Lower bound estimates of the first eigenvalue for compact manifolds with positive Ricci curvature
• Estimates on the modulus of expansion for vector fields solving nonlinear equations
• Einstein manifolds with nonnegative isotropic curvature are locally symmetric
• Proof of the fundamental gap conjecture
• Second-order Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature
• A Remark on Zhong-Yang's Eigenvalue Estimate
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