Szegö-Weinberger type inequalities for symmetric domains in simply connected space forms

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 Szegö-Weinberger type inequalities for the first $n$ positive Neumann eigenvalues.

arXiv commentThis article has been accepted for publication in the Journal of Mathematical Analysis and Applications