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Kähler Metrics with Cone Singularities and Uniqueness Problem

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

The Kähler metric with cone singularities has been the main subject which is being studied recently. In this expository note, we focus on the modular space of the Kähler metric with cone singularities. We first summary our work on the construction of the geodesic of the cone singularities. Then we apply the cone geodesic to obtain a uniqueness theorem of the constant scalar curvature Kähler metrics with cone singularities.

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Acknowledgement

The author would like to thank Professor Alexander Schmitt and the organizers of International ISAAC Congress for their invitation and hospitality.

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Authors and Affiliations

  1. Institut für Differentialgeometrie, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Kai Zheng

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  1. Kai Zheng
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Correspondence to Kai Zheng .

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Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Zheng, K. (2015). Kähler Metrics with Cone Singularities and Uniqueness Problem. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_44

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