From Local Index Theory to Bergman Kernel: A Heat Kernel Approach

Ma, Xiaonan

doi:10.1007/978-3-030-34953-0_13

Xiaonan Ma⁹

Part of the book series: Progress in Mathematics ((PM,volume 333))

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Abstract

The aim of this note is to explain a uniform approach of three different topics: Atiyah–Singer index theorem, holomorphic Morse inequalities and asymptotic expansion of Bergman kernel, by using heat kernels.

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Universit´e de Paris & Universit´e Paris Diderot – Paris 7 UFR de Math´ematiques, Case 7012 F-75205, Paris, Cedex 13, France
Xiaonan Ma

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Xiaonan Ma
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Correspondence to Xiaonan Ma .

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Editors and Affiliations

Department of Mathematics, The University of British Columbia, Vancouver, BC, Canada
Jingyi Chen
Department of Mathematics, University of Oregon, Eugene, OR, USA
Peng Lu
Department of Mathematics, University of California, Irvine, Irvine, CA, USA
Zhiqin Lu
School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia
Zhou Zhang

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Ma, X. (2020). From Local Index Theory to Bergman Kernel: A Heat Kernel Approach. In: Chen, J., Lu, P., Lu, Z., Zhang, Z. (eds) Geometric Analysis. Progress in Mathematics, vol 333. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-34953-0_13

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DOI: https://doi.org/10.1007/978-3-030-34953-0_13
Published: 11 April 2020
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-34952-3
Online ISBN: 978-3-030-34953-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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