Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

Request Permissions   Purchase Content 
 

 

The Monge-Ampère equation for $ (n-1)$-plurisubharmonic functions on a compact Kähler manifold


Authors: Valentino Tosatti and Ben Weinkove
Journal: J. Amer. Math. Soc. 30 (2017), 311-346
MSC (2010): Primary 32W20; Secondary 32U05, 32Q15, 53C55
DOI: https://doi.org/10.1090/jams/875
Published electronically: December 14, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A $ C^2$ function on $ \mathbb{C}^n$ is called $ (n-1)$-plurisubharmonic in the sense of Harvey-Lawson if the sum of any $ n-1$ eigenvalues of its complex Hessian is non-negative. We show that the associated Monge-Ampère equation can be solved on any compact Kähler manifold. As a consequence we prove the existence of solutions to an equation of Fu-Wang-Wu, giving Calabi-Yau theorems for balanced, Gauduchon, and strongly Gauduchon metrics on compact Kähler manifolds.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 32W20, 32U05, 32Q15, 53C55

Retrieve articles in all journals with MSC (2010): 32W20, 32U05, 32Q15, 53C55


Additional Information

Valentino Tosatti
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
Email: tosatti@math.northwestern.edu

Ben Weinkove
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
Email: weinkove@math.northwestern.edu

DOI: https://doi.org/10.1090/jams/875
Received by editor(s): June 12, 2013
Published electronically: December 14, 2016
Additional Notes: This research is supported in part by NSF grants DMS-1236969 and DMS-1105373. The first author is supported in part by a Sloan Research Fellowship.
Dedicated: Dedicated to Professor Duong H. Phong on the occasion of his 60th birthday
Article copyright: © Copyright 2016 American Mathematical Society