Applications of the `Ham Sandwich Theorem' to eigenvalues of the Laplacian

Abstract

We apply Gromov's ham sandwich method to get (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in a Euclidean space.

arXiv comment11pages, Example 1.2 was added (kindly informed by E. Milman). To appear in AGMS