Communications in Analysis and Geometry

Volume 23 (2015)

Number 2

Curvatures and anisometry of maps

Pages: 319 – 348

DOI: http://dx.doi.org/10.4310/CAG.2015.v23.n2.a4

Author

Benoît R. Kloeckner (Institut Fourier, Université de Grenoble I, Saint Martin d’Hères, France)

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 quasiconformal 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.

Full Text (PDF format)