PROPERTIES OF THE SOLUTIONS OF THE CONJUGATE HEAT EQUATIONS

被引:0
作者
Hamilton, Richard [1 ]
Sesum, Natasa [1 ]
机构
[1] Columbia Univ, Dept Math, New York, NY 10027 USA
基金
美国国家科学基金会;
关键词
RICCI FLOW; CONVERGENCE; MANIFOLDS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we consider the class A of those solutions u(x,t) to the conjugate heat equation partial derivative/partial derivative tu = -Delta u + Ru on compact Kahler manifolds M with c(1) > 0 (where g(t) changes by the unnormalized Kahler Ricci flow, blowing up at T < infinity), which satisfy Perelman's differential Harnack inequality (6) on [0, T]. We show A is nonempty. If vertical bar Ric (g(t))vertical bar <= C/T-1, which is always true if we have a type 1 singularity, we prove the solution u(x, t) satisfies the elliptic type Harnack inequality, with the constants that are uniform in time. If the flow g(t) has a type I singularity at T. then A has exactly one element.
引用
收藏
页码:153 / 169
页数:17
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