Mathematics > Differential Geometry
[Submitted on 4 Oct 2007]
Title:Smooth Volume Rigidity for Manifolds with Negatively Curved Targets
View PDFAbstract: We establish conditions for a continuous map of nonzero degree between a smooth closed manifold and a negatively curved manifold of dimension greater than four to be homotopic to a smooth cover, and in particular a diffeomorphism when the degree is one. The conditions hold when the volumes or entropy-volumes of the two manifolds differ by less than a uniform constant after an appropriate normalization of the metrics. The results are qualitatively sharp in the sense that the dependencies are necessary. We give a number of corollaries.
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