Spherical symmetrization and the first eigenvalue of geodesic disks on manifolds

DOI10.1007/s00526-013-0692-7zbMath1302.35275OpenAlexW1996485017MaRDI QIDQ471098

Jing Mao, Isabel Salavessa, Pedro Freitas

Publication date: 13 November 2014

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-013-0692-7

zbMATH Keywords

manifoldsLaplace-Beltrami operatorgeodesic diskfirst Dirichlet eigenvaluespherical symmetrization

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) PDEs on manifolds (35R01)

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Cites Work

• Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem
• A volume comparison estimate with radially symmetric Ricci curvature lower bound and its applications
• On surfaces with no conjugate points
• Eigenvalue comparison theorems and its geometric applications
• Spectra of domains in compact manifolds
• The spectrum of geodesic balls on spherically symmetric manifolds
• On the first twisted Dirichlet eigenvalue
• Generalized space forms
• Riemannian Geometry
• Non-Oscillation Theorems
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