C1,1 regularity for degenerate complex Monge-Ampere equations and geodesic rays

被引：30

作者：

Chu, Jianchun ^{[1
]}

Tosatti, Valentino ^{[2
]}

Weinkove, Ben ^{[2
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing, Peoples R China

[2] Northwestern Univ, Dept Math, 2033 Sheridan Rd, Evanston, IL 60208 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2018年 / 43卷 / 02期

基金：

美国国家科学基金会;

关键词：

C-1; regularity; complex Monge-Ampere equations; geodesic rays; quasi-psh envelopes; DIRICHLET PROBLEM; TEST CONFIGURATIONS; K-STABILITY; SPACE; ENVELOPES; CURVATURE; CURRENTS;

D O I：

10.1080/03605302.2018.1446167

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a C-1,C-1 estimate for solutions of complex Monge-Ampere equations on compact Kahler manifolds with possibly nonempty boundary, in a degenerate cohomology class. This strengthens previous estimates of Phong-Sturm. As applications we deduce the local C-1,C-1 regularity of geodesic rays in the space of Kahler metrics associated to a test configuration, as well as the local C-1,C-1 regularity of quasi-psh envelopes in nef and big classes away from the non-Kahler locus.

引用

页码：292 / 312

页数：21