AN INTRODUCTION TO THE CHEEGER PROBLEM

Abstract

Given a bounded domain &#937; &#8834; <B>R</B><SUP>n</SUP> with Lipschitz boundary, the Cheeger problem consists of finding a subset E of &#937; such that its ratio perimeter/volume is minimal among all subsets of &#937;. This article is a collection of some known results about the Cheeger problem which are spread in many classical and new papers.