Communications in Mathematical Physics

, Volume 274, Issue 1, pp 65–80

Mass Under the Ricci Flow

Article

DOI: 10.1007/s00220-007-0275-6

Cite this article as:
Dai, X. & Ma, L. Commun. Math. Phys. (2007) 274: 65. doi:10.1007/s00220-007-0275-6

Abstract

In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show that the mass is invariant under the flow in dimension three (similar results hold in higher dimension with more assumptions). A consequence of this result is the following. Let (M, g) be an ALE manifold of dimension n = 3. If m(g) ≠ 0, then the Ricci flow starting at g can not have Euclidean space as its (uniform) limit.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Chern Institute of MathematicsTianjinChina
  3. 3.Department of Mathematical ScienceTsinghua UniversityPekingPeople’s Republic of China