An isoperimetric inequality for Laplace eigenvalues on the sphere

Mikhail Karpukhin, Nikolai Nadirashvili, Alexei V. Penskoi +1

We show that for any positive integer k, the k-th nonzero eigenvalue of the Laplace-Beltrami operator on the two-dimensional sphere endowed with a Riemannian metric of unit area, i…