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arXiv · 1403.4197

Curvatures and anisometry of maps

Benoît Kloeckner
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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.

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Benoît Kloeckner. 2014-03-17. Curvatures and anisometry of maps. https://arxiv.org/abs/1403.4197

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