%0 Journal Article
%T Volume comparison via boundary distances
%A Sergei Ivanov
%J Mathematics
%D 2010
%I arXiv
%X The main subject of this expository paper is a connection between Gromov's filling volumes and a boundary rigidity problem of determining a Riemannian metric in a compact domain by its boundary distance function. A fruitful approach is to represent Riemannian metrics by minimal surfaces in a Banach space and to prove rigidity by studying the equality case in a filling volume inequality. I discuss recent results obtained with this approach and related problems in Finsler geometry.
%U http://arxiv.org/abs/1004.2505v1