A mass-decreasing flow in dimension three
Differential Geometry
2011-11-18 v2 General Relativity and Quantum Cosmology
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.
Keywords
Cite
@article{arxiv.1107.3220,
title = {A mass-decreasing flow in dimension three},
author = {Robert Haslhofer},
journal= {arXiv preprint arXiv:1107.3220},
year = {2011}
}
Comments
13 pages (v2: added section about continuum limit; minor additional improvements)