Estimates for the lowest Neumann eigenvalues of parallelograms and domains of constant width

Abstract

We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric inequality for parallelograms recently obtained by A. Henrot, A. Lemenant and I. Lucardesi.

arXiv comment18 pages, 1 figure. Minor edits and updated list of references. To appear in "Analysis and Mathematical Physics"