A renormalized Perelman-functional and a lower bound for the ADM-mass

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Haslhofer, Robert

关键词: Ricci flow;    Perelman-functional;    ADM-mass;   

DOI  :  10.1016/j.geomphys.2011.06.016

来源: Elsevier

【 摘 要 】

In the first part of this short article, we define a renormalized F-functional for perturbations of non-compact steady Ricci solitons. This functional motivates a stability inequality which plays an important role in questions concerning the regularity of Ricci-flat spaces and the non-uniqueness of the Ricci flow with conical initial data. In the second part, we define a geometric invariant for asymptotically flat manifolds with nonnegative scalar curvature. This invariant gives a quantitative lower bound for the ADM-mass from general relativity, motivates a Ricci flow proof of the rigidity statement in the positive mass theorem, and eventually leads to the discovery of a mass-decreasing flow in dimension three. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free