Isoperimetric Bounds for Lower Order Eigenvalues

TL;DR

This paper establishes new isoperimetric inequalities for lower order eigenvalues across various Laplacian problems on hypersurfaces and bounded domains, advancing understanding of geometric spectral bounds.

Contribution

It introduces novel isoperimetric bounds for lower order eigenvalues of Laplacian-related operators on hypersurfaces and bounded domains, expanding geometric spectral theory.

Findings

Derived new inequalities for eigenvalues of Laplacian on hypersurfaces

Established bounds for biharmonic Steklov problems

Proposed open questions for future research

Abstract

New isoperimetric inequalities for lower order eigenvalues of the Laplacian on closed hypersurfaces, of the biharmonic Steklov problems and of the Wentzell-Laplace on bounded domains in a Euclidean space are proven. Some open questions for further study are also proposed.