No breathers theorem for some noncompact Ricci flows
Differential Geometry
2013-08-19 v2 Analysis of PDEs
Abstract
Under suitable conditions near infinity and assuming boundedness of curvature tensor, we prove a no breathers theorem in the spirit of Ivey-Perelman for some noncompact Ricci flows. These include Ricci flows on asymptotically flat (AF) manifolds with positive scalar curvature. Since the method for the compact case faces a difficulty, the proof involves solving a new non-local elliptic equation which is the Euler-Lagrange equation of a scaling invariant log Sobolev inequality.
Cite
@article{arxiv.1205.0334,
title = {No breathers theorem for some noncompact Ricci flows},
author = {Qi S. Zhang},
journal= {arXiv preprint arXiv:1205.0334},
year = {2013}
}
Comments
More references and motivations from irreversibility of world sheet added following referees' suggestions; to appear in Asian J. Math