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Spherical Cones: Classification and a Volume Minimization Principle

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Abstract

Using a variational approach, we establish the equivalence between a weighted volume minimization principle and the existence of a conical Calabi–Yau structure on horospherical cones with mild singularities. This allows us to do explicit computations on the examples arising from rank-two symmetric spaces, showing the existence of many irregular horospherical cones.

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Acknowledgements

This paper is part of a thesis prepared under the supervision of Thibaut Delcroix and Marc Herzlich, partially supported by ANR-21-CE40-0011 JCJC project MARGE. I would like to thank Thibaut Delcroix for many illuminating discussions and remarks.

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Funding was provided by Université de Montpellier.

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  1. IMAG, Univ Montpellier, CNRS, Montpellier, France

    Tran-Trung Nghiem

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Nghiem, TT. Spherical Cones: Classification and a Volume Minimization Principle. J Geom Anal 33, 221 (2023). https://doi.org/10.1007/s12220-023-01286-x

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