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On Curvature Estimates of Bounded Domains

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Complex Analysis and Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 144))

Abstract

We consider the Bergman curvatures estimate for bounded domains in terms of the squeezing function. As applications, we give the asymptotic boundary behaviors of the curvatures near strictly pseudoconvex boundary points, using a recent result given by Fornaess and Wold.

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Acknowledgments

The author is grateful to the organizers of the 10\(^{\text {th}}\) Korean Conference on Several Complex Variables, especially Prof. K.-T. Kim and Prof. N. Shcherbina, for their kind invitation. He would also like to thank Prof. Q.-K. Lu for many invaluable communications on this topic. Project partially supported by NSFC (No. 11371025, 11371257).

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Authors and Affiliations

  1. School of Mathematical Science, Capital Normal University, Beijing, 100048, People’s Republic of China

    Liyou Zhang

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  1. Liyou Zhang
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Correspondence to Liyou Zhang .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

  2. Dept. of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  3. Université Joseph Fourier Grenoble, Institut Fourier, Grenoble, France

    Hervé Gaussier

  4. Graduate School of Mathematical Sciences, The University of Tokyo, Meguro-ku, Tokyo, Japan

    Kengo Hirachi

  5. Department of Mathematics, POSTECH, Pohang, Korea (Republic of)

    Kang-Tae Kim

  6. Department of Mathematics, Bergische Universität Wuppertal, Wuppertal, Nordrhein-Westfalen, Germany

    Nikolay Shcherbina

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Zhang, L. (2015). On Curvature Estimates of Bounded Domains. In: Bracci, F., Byun, J., Gaussier, H., Hirachi, K., Kim, KT., Shcherbina, N. (eds) Complex Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 144. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55744-9_27

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