Volume comparison via boundary distances
Differential Geometry
2010-04-16 v1 Metric Geometry
Abstract
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.
Cite
@article{arxiv.1004.2505,
title = {Volume comparison via boundary distances},
author = {Sergei Ivanov},
journal= {arXiv preprint arXiv:1004.2505},
year = {2010}
}
Comments
ICM 2010 sectional talk paper