A Reilly type integral inequality for the \(p\)-Laplacian and applications to submanifolds of the unit sphere

DOI10.1007/s13398-024-01563-6zbMATH Open1537.53017MaRDI QIDQ6542367

Fábio R. dos Santos, Matheus N. Soares

Publication date: 22 May 2024

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

zbMATH Keywords

\(p\)-Laplacianestimates for eigenvaluescompact submanifodsReilly integral inequality

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Local Riemannian geometry (53B20) Inequalities and extremum problems in real or complex geometry (51M16)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp estimate on the first eigenvalue of the \(p\)-Laplacian
• A maximum principle for hypersurfaces with constant scalar curvature and applications
• Geometric applications of the solvability of Neumann problems on a Riemannian manifold
• Minimal submanifolds in a sphere
• The first eigenvalue of the \(p\)-Laplacian on a compact Riemannian manifold.
• Sharp estimates on the first eigenvalue of the \(p\)-Laplacian with negative Ricci lower bound
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• Some applications of Bochner formula to submanifolds of a unit sphere
• Uniqueness theorems on conformal deformation of metrics, sobolev inequalities, and an eigenvalue estimate
• An Estimate on the Ricci Curvature of a Submanifold and Some Applications
• Lower bounds for the length of the second fundamental form via the first eigenvalue of the \(p\)-Laplacian

This page was built for publication: A Reilly type integral inequality for the \(p\)-Laplacian and applications to submanifolds of the unit sphere