Hessian equations on closed Hermitian manifolds

Dekai Zhang

Vol. 291 (2017), No. 2, 485–510

DOI: 10.2140/pjm.2017.291.485

Abstract

We solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the Kähler case proven by Hou, Ma and Wu and Dinew and Kołodziej. Solving the equation can be reduced to the derivation of a priori second-order estimates. We introduce a new method to prove the $C^0$ estimate. The $C^2$ estimate can be derived if we use the auxiliary function which is mainly due to Hou, Ma and Wu and Tosatti and Weinkove.

Keywords

Hessian equations, closed Hermitian manifolds, a priori estimates

Mathematical Subject Classification 2010

Primary: 35J60, 53C55

Milestones

Received: 30 October 2015

Revised: 18 January 2017

Accepted: 2 May 2017

Published: 14 September 2017