Curvatures and anisometry of maps
Differential Geometry
2014-03-18 v1
Abstract
We prove various inequalities measuring how far from an isometry a local map from a manifold of high curvature to a manifold of low curvature must be. We consider the cases of volume-preserving, conformal and quasi-conformal maps. The proofs relate to a conjectural isoperimetric inequality for manifolds whose curvature is bounded above, and to a higher-dimensional generalization of the Schwarz-Ahlfors lemma.
Keywords
Cite
@article{arxiv.1403.4197,
title = {Curvatures and anisometry of maps},
author = {Benoît Kloeckner},
journal= {arXiv preprint arXiv:1403.4197},
year = {2014}
}