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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The Monge-Ampère equation for $(n-1)$-plurisubharmonic functions on a compact Kähler manifold
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by Valentino Tosatti and Ben Weinkove PDF
J. Amer. Math. Soc. 30 (2017), 311-346 Request permission

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.
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Additional Information
  • Valentino Tosatti
  • Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
  • MR Author ID: 822462
  • Email: tosatti@math.northwestern.edu
  • Ben Weinkove
  • Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
  • Email: weinkove@math.northwestern.edu
  • 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
  • © Copyright 2016 American Mathematical Society
  • 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
  • MathSciNet review: 3600038