Mass under the Ricci flow

Xianzhe Dai; Li Ma

Mass under the Ricci flow

Differential Geometry 2007-05-23 v1

Authors: Xianzhe Dai , Li Ma

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 $m(g)\neq 0$ , then the Ricci flow starting at $g$ can not have Euclidean space as its (uniform) limit.

Keywords

ricci flow

Cite

@article{arxiv.math/0510083,
  title  = {Mass under the Ricci flow},
  author = {Xianzhe Dai and Li Ma},
  journal= {arXiv preprint arXiv:math/0510083},
  year   = {2007}
}

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