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Transactions of the American Mathematical Society

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Abstract Bergman kernel expansion and its applications

Authors: Chiung-ju Liu and Zhiqin Lu
Journal: Trans. Amer. Math. Soc. 368 (2016), 1467-1495
MSC (2010): Primary 32Q15; Secondary 53A30
Published electronically: July 9, 2015
MathSciNet review: 3430370
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Abstract: We give a purely complex geometric proof of the existence of the Bergman kernel expansion. Our method actually provides a sharper estimate, and in the case that the metrics are real analytic, we prove that the remainder decays faster than any polynomial.

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Chiung-ju Liu
Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan 106

Zhiqin Lu
Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875

Keywords: Szeg\H{o} kernel, asymptotic expansion, ample line bundle
Received by editor(s): May 15, 2014
Received by editor(s) in revised form: November 11, 2014
Published electronically: July 9, 2015
Additional Notes: The first author was supported by NSC grant 982115M002007 in Taiwan. The second author was partially supported by NSF grant DMS-12-06748.
Article copyright: © Copyright 2015 American Mathematical Society

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