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On the constant scalar curvature Kähler metrics (I)—A priori estimates


Authors: Xiuxiong Chen and Jingrui Cheng
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
Published electronically: June 7, 2021
MathSciNet review: 4301557
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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
Article copyright: © Copyright 2021 American Mathematical Society