15 January 2012 Differentiable rigidity under Ricci curvature lower bound
L. Bessières, G. Besson, G. Courtois, S. Gallot
Duke Math. J. 161(1): 29-67 (15 January 2012). DOI: 10.1215/00127094-1507272

Abstract

In this article we prove a differentiable rigidity result. Let (Y,g) and (X,g0) be two closed n-dimensional Riemannian manifolds (n3), and let f:YX be a continuous map of degree 1. We furthermore assume that the metric g0 is real hyperbolic and denote by d the diameter of (X,g0). We show that there exists a number ε:=ε(n,d)>0 such that if the Ricci curvature of the metric g is bounded below by (n1)g and its volume satisfies volg(Y)(1+ε)volg0(X), then the manifolds are diffeomorphic. The proof relies on Cheeger–Colding’s theory of limits of Riemannian manifolds under lower Ricci curvature bound.

Citation

Download Citation

L. Bessières. G. Besson. G. Courtois. S. Gallot. "Differentiable rigidity under Ricci curvature lower bound." Duke Math. J. 161 (1) 29 - 67, 15 January 2012. https://doi.org/10.1215/00127094-1507272

Information

Published: 15 January 2012
First available in Project Euclid: 30 December 2011

zbMATH: 1250.53033
MathSciNet: MR2872553
Digital Object Identifier: 10.1215/00127094-1507272

Subjects:
Primary: 53C20
Secondary: 53C35

Rights: Copyright © 2012 Duke University Press

Vol.161 • No. 1 • 15 January 2012
Back to Top