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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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On the constant scalar curvature Kähler metrics (I)—A priori estimates
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by Xiuxiong Chen and Jingrui Cheng HTML | PDF
J. Amer. Math. Soc. 34 (2021), 909-936 Request permission

Abstract:

In this paper, we derive apriori estimates for constant scalar curvature Kähler metrics on a compact Kähler manifold. We show that higher order derivatives can be estimated in terms of a $C^0$ bound for the Kähler potential.
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Additional Information
  • Xiuxiong Chen
  • Affiliation: Institute of Geometry and Physics, University of Science and Technology of China, No. 96 Jinzhai Road, Hefei, Anhui, 230026, China AND Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, USA
  • MR Author ID: 632654
  • Email: xiu@math.sunysb.edu
  • Jingrui Cheng
  • Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI, 53706, USA AND Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, USA
  • MR Author ID: 1185151
  • Email: jingrui.cheng@stonybrook.edu
  • Received by editor(s): February 27, 2018
  • Received by editor(s) in revised form: February 24, 2020, June 3, 2020, and July 26, 2020
  • Published electronically: June 7, 2021
  • Additional Notes: The first named author was partially supported by NSF grant DMS-1515795 and Simons Foundation grant 605796

  • Dedicated: Dedicated to Sir Simon Donaldson for his 60th birthday
  • © Copyright 2021 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 34 (2021), 909-936
  • MSC (2020): Primary 53C21, 53C55; Secondary 35J30, 35J60, 35J96
  • DOI: https://doi.org/10.1090/jams/967
  • MathSciNet review: 4301557