Singular Ricci flows I

被引：39
作者：
Kleiner, Bruce [1 ]
Lott, John [2 ]
机构：
[1] Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA
[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
来源：
ACTA MATHEMATICA | 2017年 / 219卷 / 01期
关键词：
MEAN-CURVATURE FLOW; HARMONIC MAPS; PARTIAL REGULARITY; REDUCED VOLUME; LEVEL SETS; EXISTENCE; SURFACES; MOTION; 2-ORBIFOLDS; 4-MANIFOLDS;
D O I：
10.4310/ACTA.2017.v219.n1.a4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. These provide a solution to the long-standing problem of finding a good notion of Ricci flow through singularities, in the 3-dimensional case. We prove that Ricci flow with surgery, starting from a fixed initial condition, subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows. © 2017 by Institut Mittag-Leffler. All rights reserved.
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页码：65 / 134
页数：70
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