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The partial $ C^0$-estimate along the continuity method


Author: Gábor Székelyhidi
Journal: J. Amer. Math. Soc. 29 (2016), 537-560
MSC (2010): Primary 53C55; Secondary 53C23
DOI: https://doi.org/10.1090/jams/833
Published electronically: April 29, 2015
MathSciNet review: 3454382
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Abstract: We prove that the partial $ C^0$-estimate holds for metrics along Aubin's continuity method for finding Kähler-Einstein metrics, confirming a special case of a conjecture due to Tian. We use the method developed in recent work of Chen-Donaldson-Sun on the analogous problem for conical Kähler-Einstein metrics.


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Gábor Székelyhidi
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: gszekely@nd.edu

DOI: https://doi.org/10.1090/jams/833
Received by editor(s): November 5, 2013
Received by editor(s) in revised form: June 26, 2014, and March 18, 2015
Published electronically: April 29, 2015
Additional Notes: The author was supported in part by NSF grant DMS-1306298.
Article copyright: © Copyright 2015 American Mathematical Society