Sets of finite perimeter and geometric variational problems: an introduction to Geometric Measure Theory

Abstract: This is a book about sets of finite perimeter and their applications to the study of isoperimetric-type problems, published as Cambridge Studies in Advanced Mathematics no. 135. The aim of the book is to introduce the reader to a set of crucial ideas and techniques that are needed to discuss the existence and regularity properties of minimizers in geometric variational problems, as well as in the description of their qualitative properties, like symmetry, boundedness, convexity, etc. The book is divided in four parts, opened by rather detailed synopses, which are contained in attached extract of the book.