On Feldman-Ilmanen-Knopf's conjecture for the blow-up behavior of the Kahler Ricci flow

被引：3
|
作者：
Guo, Bin [1 ,2 ]
Song, Jian [1 ]
机构：
[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA
[2] Columbia Univ, Dept Math, New York, NY 10027 USA
来源：
MATHEMATICAL RESEARCH LETTERS | 2016年 / 23卷 / 06期
基金：
美国国家科学基金会;
关键词：
CONTRACTING EXCEPTIONAL DIVISORS; CURVATURE; SOLITONS; MANIFOLDS; SHRINKING; SURFACES;
D O I：
10.4310/MRL.2016.v23.n6.a6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the Ricci flow on CPn blown-up at one point starting with any U(n)-invariant Kahler metric. It is proved in [9, 22, 32] that the Kahler-Ricci flow must develop Type I singularities. We show that if the total volume does not go to zero at the singular time, then any Type I parabolic blow-up limit of the Ricci flow along the exceptional divisor is the unique U(n)-complete shrinking Kahler-Ricci soliton on C-n blown-up at one point. This establishes the conjecture of Feldman-Ilmanen-Knopf [8].
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页码：1681 / 1719
页数：39
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