Weak solutions to degenerate complex Monge-Ampere flows II

被引：22

作者：

Eyssidieux, Philippe ^{[1
,2
]}

Guedj, Vincent ^{[2
,3
]}

Zeriahi, Ahmed ^{[3
]}

机构：

[1] Univ Grenoble 1, F-38041 Grenoble, France

[2] Inst Univ France, Paris, France

[3] Inst Math Toulouse, Toulouse, France

来源：

ADVANCES IN MATHEMATICS | 2016年 / 293卷

关键词：

Complex Monge-Ampere flows; Kahler-Ricci flow; Canonical singularities; Viscosity solutions; VISCOSITY SOLUTIONS;

D O I：

10.1016/j.aim.2016.02.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Studying the (long-term) behavior of the Kahler-Ricci flow on mildly singular varieties, one is naturally led to study weak solutions of degenerate parabolic complex Monge-Ampere equations. The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for degenerate complex Monge-Ampere flows on compact Kahler manifolds. Our general theory allows in particular to define and study the (normalized) Kahler-Ricci flow on varieties with canonical singularities, generalizing results of Song and Tian. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：37 / 80

页数：44

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