Inserted: 6 jul 2010
Last Updated: 10 feb 2015
Journal: Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)
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.