Isoperimetric Inequalities in Analysis and Geometry

University Of Chicago, Chicago IL

Investigators

Abstract

ABSTRACT DMS - 0204650. We plan to study isoperimetric inequalities for Dirichlet eigenvalues of biharmonic operator in dimensions greater than 3, for the sums of reciprocals Neumann eigenvalues, for the Willmore functional of a surface, isoperimetric inequalities for Dirichlet Laplacian with Bonnesen type term. By isoperimetric inequality we mean any inequality relating two or more domain functionals (defined on the same domain) which is such that the equality sign actually holds for some domain of the class under consideration (or in some appropriate limiting sense). There are still some open fundamental questions in this classical area.