Dimensional reduction and the long-time behavior of Ricci flow

被引：34
作者：
Lott, John [1 ]
机构：
[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
来源：
COMMENTARII MATHEMATICI HELVETICI | 2010年 / 85卷 / 03期
关键词：
Ricci flow; geometrization; COLLAPSING RIEMANNIAN-MANIFOLDS; FUNDAMENTAL-GROUPS; QUASI-CONVERGENCE; EXTINCTION TIME; 3-MANIFOLDS; GEOMETRIES; METRICS;
D O I：
10.4171/CMH/203
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that are O(t(-1)) and diameter that is O(t(1/2)), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.
引用
收藏
页码：485 / 534
页数：50
相关论文
共 54 条
[1]  
[Anonymous], 1999, Metric structures for Riemannian and nonRiemannian spaces
[2]  
[Anonymous], 1957, B SOC MATH FR
[3]   Collapsing irreducible 3-manifolds with nontrivial fundamental group [J].
Bessieres, L. ;
Besson, G. ;
Boileau, M. ;
Maillot, S. ;
Porti, J. .
INVENTIONES MATHEMATICAE, 2010, 179 (02) :435-460
[4]  
BRIDSON M, 1999, GRUNDLEHREN MATH, V319
[5]  
CHEEGER J, 1986, J DIFFER GEOM, V23, P309
[6]  
CHEEGER J, 1990, J DIFFER GEOM, V32, P269
[7]   COLLAPSED RIEMANNIAN-MANIFOLDS WITH BOUNDED DIAMETER AND BOUNDED COVERING GEOMETRY [J].
CHEEGER, J ;
RONG, X .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 1995, 5 (02) :141-163
[8]  
Cheeger J., 1992, J AM MATH SOC, V5, P327
[9]  
Cheeger Jeff., 1971, J. Differential Geometry, V6, P119, DOI 10.4310/jdg/1214430220
[10]  
Chow B., 2007, The Ricci flow: techniques and applications, V135
123456