On a complex Hessian flow

Weimin Sheng and Jiaxiang Wang

Vol. 300 (2019), No. 1, 159–177

DOI: 10.2140/pjm.2019.300.159

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