Applications of the `Ham Sandwich Theorem' to eigenvalues of the   Laplacian
  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. 
Kei Funano
math.DG math.FA math.SP