Calculus of Variations and Geometric Measure Theory

A. Lemenant

A presentation of the average distance minimizing problem

created by lemenant on 06 Jul 2010
modified on 10 Feb 2015


review paper

Inserted: 6 jul 2010
Last Updated: 10 feb 2015

Journal: Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)
Year: 2011


The purpose of these notes is to present an overview of the fascinating ''average distance problem'', and more specifically about regularity results. We shall state the main known results without writing the proofs in full details but trying to explain for each of them the key ideas and giving a lot of comments.