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arXiv · 1107.3220

A mass-decreasing flow in dimension three

Robert Haslhofer
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Abstract

In this article, we introduce a mass-decreasing flow for asymptotically flat three-manifolds with nonnegative scalar curvature. This flow is defined by iterating a suitable Ricci flow with surgery and conformal rescalings and has a number of nice properties. In particular, wormholes pinch off and nontrivial spherical space forms bubble off in finite time. Moreover, a noncompact variant of the Perelman-energy is monotone along the flow. Assuming a certain inequality between the mass and this Perelman-energy a priori, we can prove that the flow squeezes out all the initial mass.

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Robert Haslhofer. 2011-11-17. A mass-decreasing flow in dimension three. https://arxiv.org/abs/1107.3220

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