Pure and Applied Mathematics Quarterly
Volume 17 (2021)
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
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.
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