Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 3

Special Issue in Honor of Duong H. Phong

Edited by Tristan Collins, Valentino Tosatti, and Ben Weinkove

The complex Monge–Ampère equation with a gradient term

Pages: 1005 – 1024

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n3.a7

Authors

Valentino Tosatti (Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada; and Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

Ben Weinkove (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

Abstract

We consider the complex Monge–Ampère equation with an additional linear gradient term inside the determinant. We prove existence and uniqueness of solutions to this equation on compact Hermitian manifolds.

Full Text (PDF format)

V. Tosatti was partially supported by NSF grants DMS-1610278 and DMS-1903147. Part of this work was done while visiting the Center for Mathematical Sciences and Applications at Harvard University, which he thanks for the hospitality.

B. Weinkove was partially supported by NSF grant DMS-1709544.

Received 11 May 2019

Accepted 23 June 2019

Published 14 June 2021