Luigi Provenzano

Maximisers for the second Neumann eigenvalue of annuli in two-dimensional space forms

We prove a sharp Szeg\"o-Weinberger-type inequality for balanced doubly connected domains in $\mathbb S^2$, $\mathbb R^2$ and $\mathbb H^2$. More precisely, the first positive Neumann eigenvalue is bounded above by that of the corresponding rotationally symmetric annulus, determined by the area of the domain and the ar...