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Positivity and Completeness of Invariant Metrics

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Abstract

We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains in \(\mathbb {C}^n\). As an application, we establish a method for showing the positivity and completeness of invariant metrics including the Bergman metric mainly for the unbounded domains.

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Acknowledgments

We would like to thank the referee for his valuable comments. Research of Taeyong Ahn and Kang-Tae Kim is supported in part by the Grant 2011-0030044 (The SRC-GAIA) of the NRF of Korea.

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Authors and Affiliations

  1. Center for Geometry and its Applications, POSTECH, Pohang, 790-784, The Republic of Korea

    Taeyong Ahn

  2. Univ. Grenoble Alpes, IF, 38000, Grenoble, France

    Hervé Gaussier

  3. CNRS, IF, 38000, Grenoble, France

    Hervé Gaussier

  4. Center for Geometry and its Applications and Department of Mathematics, POSTECH, Pohang, 790-784, The Republic of Korea

    Kang-Tae Kim

Authors
  1. Taeyong Ahn
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  2. Hervé Gaussier
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  3. Kang-Tae Kim
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Correspondence to Hervé Gaussier.

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Ahn, T., Gaussier, H. & Kim, KT. Positivity and Completeness of Invariant Metrics. J Geom Anal 26, 1173–1185 (2016). https://doi.org/10.1007/s12220-015-9587-5

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  • DOI: https://doi.org/10.1007/s12220-015-9587-5

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