A TYPE OF PARABOLIC FLOW WITH MIXED HESSIANS ON COMPACT KAHLER MANIFOLDS

被引：0

作者：

Tsai, Yi-Lin ^{[1
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92618 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 01期

关键词：

NONLINEAR ELLIPTIC-EQUATIONS; MONGE-AMPERE EQUATION; COMPLEX; CONVERGENCE; CURVATURE;

D O I：

10.1090/proc/16097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the solvability of a general class of mixed Hessian type equations on compact Kahler manifolds. Based on an observation in Guan and Zhang [Pure Appl. Math. Q. 17 (2021), pp. 865-907], the mixed Hessian equations can be rewritten as elliptic and concave equations which satisfy the general framework in Szekelyhidi [J. Differential Geom. 109 (2018), pp. 337-378] and Phong and To [Ann. Sci. Ec. Norm. Super. (4) 54 (2021), pp. 793-829] except one condition. We notice that the absence of this condition can be overcome by using the particular structure of the mixed Hessian equations. As an application, the solvability of the deformed Hermitian Yang-Mills equations in dimension three was also studied.

引用

页码：425 / 437

页数：13

共 32 条

[1]

[Anonymous], 1999, ASIAN J. MATH

[2] Weak solutions to the complex Hessian equation [J].