Differentiable Rigidity under Ricci curvature lower bound

Details Differentiable Rigidity under Ricci curvature lower bound Differentiable Rigidity under Ricci curvature lower bound

2008-05-25

arxiv.org/abs/0805.3845v2

Mathematics

Differential Geometry

33 pages, 1 dessin

Scientific paper

In this article we prove a differentiable rigidity result. Let $(Y, g)$ and $(X, g_0)$ be two closed $n$-dimensional Riemannian manifolds ($n\geqslant 3$) and $f:Y\to X$ be a continuous map of degree $1$. We furthermore assume that the metric $g_0$ is real hyperbolic and denote by $d$ the diameter of $(X,g_0)$. We show that there exists a number $\varepsilon:=\varepsilon (n, d)>0$ such that if the Ricci curvature of the metric $g$ is bounded below by $-n(n-1)$ and its volume satisfies $\vol_g (Y)\leqslant (1+\varepsilon) \vol_{g_0} (X)$ then the manifolds are diffeomorphic. The proof relies on Cheeger-Colding's theory of limits of Riemannian manifolds under lower Ricci curvature bound.

Affiliated with

Also associated with

No associations

Rating

Differentiable Rigidity under Ricci curvature lower bound does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Differentiable Rigidity under Ricci curvature lower bound, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differentiable Rigidity under Ricci curvature lower bound will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-437480