Vol. 276, No. 2, 2015

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ISSN: 0030-8730
The complex Monge–Ampère equation on some compact Hermitian manifolds

Jianchun Chu

Vol. 276 (2015), No. 2, 369–386
Abstract

We consider the complex Monge–Ampère equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension 2) or a Hermitian metric satisfying an additional condition (in higher dimensions). We prove that the Laplacian estimate holds when F is in W1,q0 for any q0 > 2n. As an application, we show that, up to scaling, there exists a unique classical solution in W3,q0 for the complex Monge–Ampère equation when F is in W1,q0.

Keywords
complex Monge–Ampère equation, compact Hermitian manifold
Mathematical Subject Classification 2010
Primary: 35J96, 53C55
Milestones
Received: 15 May 2014
Revised: 22 October 2014
Accepted: 23 December 2014
Published: 15 July 2015
Authors
Jianchun Chu
School of Mathematical Sciences
Peking University
Yiheyuan Road 5
Beijing, 100871
China