The J-equation and the supercritical deformed Hermitian-Yang-Mills equation

被引：31
作者：
Chen, Gao [1 ]
机构：
[1] Univ Sci & Technol China, Inst Geometry & Phys, 96 Jinzhai Rd, Hefei, Anhui, Peoples R China
来源：
INVENTIONES MATHEMATICAE | 2021年 / 225卷 / 02期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/s00222-021-01035-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove that for any Kahler metrics omega(0) and chi on M, there exists a Kahler metric omega(phi) = omega(0) + root-1 partial derivative(partial derivative) over bar phi > 0 satisfying the J-equation tr omega(phi)chi = c if and only if (M, [omega(0)], [chi]) is uniformly J-stable. As a corollary, we find a sufficient condition for the existence of constant scalar curvature Kahler metrics with c(1) < 0. Using the same method, we also prove a similar result for the supercritical deformed Hermitian-Yang-Mills equation.
引用
收藏
页码：529 / 602
页数：74
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