An alternative proof of a rigidity theorem for the sharp Sobolev constant
Differential Geometry
2010-02-22 v2
Abstract
We provide a somewhat geometric proof of a rigidity theorem by M. Ledoux and C. Xia concerning complete manifolds with non-negative Ricci curvature supporting an Euclidean-type Sobolev inequality with (almost) best Sobolev constant. Using the same technique we also generalize Ledoux-Xia result to complete manifolds with asymptotically non-negative curvature.
Cite
@article{arxiv.1002.0756,
title = {An alternative proof of a rigidity theorem for the sharp Sobolev constant},
author = {Stefano Pigola and Giona Veronelli},
journal= {arXiv preprint arXiv:1002.0756},
year = {2010}
}
Comments
11 pages. Corrected typos. Added a new result concerning rigidity of manifolds with asymptotically non-negative curvature