Pluripotential Monge-Ampere flows in big cohomology classes

被引：3
|
作者：
Dang, Quang-Tuan [1 ,2 ]
机构：
[1] Univ Paris Saclay, Lab Math Orsay, CNRS, F-91405 Orsay, France
[2] Univ Toulouse, Inst Math Toulouse, CNRS, 118 Route Narbonne, F-31400 Toulouse, France
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2022年 / 282卷 / 06期
关键词：
Parabolic Monge-Ampere equation; Big cohomology class; Kahler-Ricci flow; KAHLER-EINSTEIN METRICS; DIRICHLET PROBLEM; MINIMAL MODELS; RICCI FLOW; VARIETIES; EXISTENCE;
D O I：
10.1016/j.jfa.2021.109373
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study pluripotential complex Monge-Ampere flows in big cohomology classes on compact Kahler manifolds. We use the Perron method, considering pluripotential subsolutions to the Cauchy problem. We prove that, under natural assumptions on the data, the upper envelope of all subsolutions is continuous in space and semi-concave in time, and provides a unique pluripotential solution with such regularity. We apply this theory to study pluripotential Kahler-Ricci flows on compact Kahler manifolds of general type as well as on stable varieties (c) 2021 Elsevier Inc. All rights reserved.
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页数：65
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