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Uniqueness of some Calabi–Yau metrics on \({\mathbf {C}}^{{n}}\)

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Abstract

We consider the Calabi–Yau metrics on \(\mathbf {C}^n\) constructed recently by Yang Li, Conlon–Rochon, and the author, that have tangent cone \(\mathbf {C}\times A_1\) at infinity for the \((n-1)\)-dimensional Stenzel cone \(A_1\). We show that up to scaling and isometry this Calabi–Yau metric on \(\mathbf {C}^n\) is unique. We also discuss possible generalizations to other manifolds and tangent cones.

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Acknowledgements

I would like to thank Nick Edelen and Gang Liu for insightful discussions, as well as Shih-Kai Chiu and Yang Li for helpful comments on an earlier draft of the paper.

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  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Gábor Székelyhidi

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  1. Gábor Székelyhidi
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Correspondence to Gábor Székelyhidi.

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The author is supported in part by NSF Grants DMS-1350696 and DMS-1906216

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Székelyhidi, G. Uniqueness of some Calabi–Yau metrics on \({\mathbf {C}}^{{n}}\). Geom. Funct. Anal. 30, 1152–1182 (2020). https://doi.org/10.1007/s00039-020-00543-3

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  • DOI: https://doi.org/10.1007/s00039-020-00543-3

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