Szeg\"{o}-Weinberger type inequalities for symmetric domains in simply connected space forms

TL;DR

This paper establishes Szeg"o-Weinberger type inequalities for the first several Neumann eigenvalues of the Laplacian on symmetric, multi-connected domains within simply connected space forms, extending classical spectral bounds.

Contribution

It introduces new inequalities for Neumann eigenvalues on symmetric multi-connected domains in space forms, generalizing existing results to more complex geometries.

Findings

Proved inequalities for the first n positive Neumann eigenvalues.

Extended classical bounds to multi-connected domains.

Applied symmetry assumptions to derive spectral inequalities.

Abstract

We consider the Neumann eigenvalue problem for Laplacian on a bounded multi-connected domain contained in simply connected space forms. Under certain symmetry assumptions on the domain, we prove Szeg\"{o}-Weinberger type inequalities for the first $n$ positive Neumann eigenvalues.