Spherical caps do not always maximize Neumann eigenvalues on the sphere

Dorin Bucur, Richard S. Laugesen, Eloi Martinet +1

We prove the existence of an open set $\hat{I}\text{c◯}\subset {\mathbb{S}}^2$ for which the first positive eigenvalue of the Laplacian with Neumann boundary condition exceeds that of the geodesic…