Mini-Workshop: Shape Analysis for Eigenvalues

Abstract

The main goal of the meeting was to bring together two mathematical communities working on the shape analysis of eigenvalues by quite different methods. On the one hand explicit solutions to optimal shape problems for eigenvalues are searched by means of direct estimations, symmetrizations, rearrangements; on the other hand recent techniques of variational type have been developed to prove the existence of an optimal shape and intensive research is carried out to prove the regularity of the free boundary and to analyze the optimality