Escobar's conjecture on a sharp lower bound for the first nonzero Steklov eigenvalue

DOI10.1007/s42543-023-00068-2MaRDI QIDQ6615575

Changwei Xiong, Chao Xia

Publication date: 8 October 2024

Published in: Peking Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Laplacian eigenvalueSteklov eigenvaluesharp boundnonnegative sectional curvature

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Eigenvalue problems for linear operators (47A75) Variational methods for eigenvalues of operators (49R05)

Related Items (1)

An upper bound for the first nonzero Steklov eigenvalue

Cites Work

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• A sharp comparison theorem for compact manifolds with mean convex boundary
• On the first eigenvalue of the Dirichlet-to-Neumann operator on forms
• Sharp bounds for the first non-zero Stekloff eigenvalues
• An optimal Poincaré inequality for convex domains
• Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes
• Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary
• \(C^\infty\) convex functions and manifolds of positive curvature
• An elementary method in the study of nonnegative curvature
• An isoperimetric inequality and the first Steklov eigenvalue
• Metrics with nonnegative isotropic curvature
• Self-duality and 4-manifolds with nonnegative curvature on totally isotropic 2-planes
• The geometry of the first non-zero Stekloff eigenvalue
• Sur les problèmes fondamentaux de la physique mathématique.
• Weyl-type bounds for Steklov eigenvalues
• Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds
• Comparison of Steklov eigenvalues on a domain and Laplacian eigenvalues on its boundary in Riemannian manifolds
• Partial differential equations. 2: Qualitative studies of linear equations
• The Obata equation with Robin boundary condition
• On the spectra of three Steklov eigenvalue problems on warped product manifolds
• The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript
• The Steklov and Laplacian spectra of Riemannian manifolds with boundary
• Spectral geometry of the Steklov problem (survey article)
• A higher dimensional generalization of Hersch-Payne-Schiffer inequality for Steklov eigenvalues
• A Generalization of Reilly's Formula and its Applications to a New Heintze–Karcher Type Inequality
• Proof of the fundamental gap conjecture
• $C^\infty$ approximations of convex, subharmonic, and plurisubharmonic functions
• The Legacy of Vladimir Andreevich Steklov
• A general comparison theorem with applications to volume estimates for submanifolds
• Riemannian Geometry
• The Lipschitz continuity of the distance function to the cut locus
• The problem of optimal smoothing for convex functions
• Some Isoperimetric Inequalities for Harmonic Functions

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