Mathematical Research Letters

Volume 29 (2022)

Number 6

Complex Monge–Ampère equations with solutions in finite energy classes

Pages: 1659 – 1683



Duc Thai Do (Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam)

Duc-Viet Vu (Department of Mathematics and Computer Science, Division of Mathematics, University of Cologne, Germany)


We characterize the class of probability measures on a compact Kähler manifold such that the associated Monge–Ampère equation has a solution of finite pluricomplex energy. Our results are also valid in the big cohomology class setting.

Received 12 November 2020

Accepted 1 June 2021

Published 4 May 2023