Vol. 300, No. 1, 2019

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On a complex Hessian flow

Weimin Sheng and Jiaxiang Wang

Vol. 300 (2019), No. 1, 159–177
Abstract

We consider a gradient flow generated by a complex Hessian functional which is defined on compact Kähler manifolds. By setting up the a priori estimates of the admissible solutions, we prove the long-time existence of the solution to the flow and its convergence. Thus we show the functional admits a local minimal point in the space of admissible functions. As its application, we show the solvability of a class of complex Hessian equations.

Keywords
fully nonlinear flow, complex Hessian equation
Mathematical Subject Classification 2010
Primary: 35K55, 53C44, 53C55
Milestones
Received: 6 January 2018
Revised: 14 August 2018
Accepted: 22 August 2018
Published: 20 July 2019
Authors
Weimin Sheng
School of Mathematical Sciences
Zhejiang University
Hangzhou
China
Jiaxiang Wang
School of Mathematical Sciences
Zhejiang University
Hangzhou
China