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arXiv · 2206.08210

Nonuniqueness of Calabi-Yau metrics with maximal volume growth

Shih-Kai Chiu
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Abstract

We construct a family of inequivalent Calabi-Yau metrics on $\mathbf{C}^3$ asymptotic to $\mathbf{C} \times A_2$ at infinity, in the sense that any two of these metrics cannot be related by a scaling and a biholomorphism. This provides the first example of families of Calabi-Yau metrics asymptotic to a fixed tangent cone at infinity, while keeping the underlying complex structure fixed. We propose a refinement of a conjecture of Sz\'ekelyhidi addressing the classification of such metrics.

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Shih-Kai Chiu. 2022-06-16. Nonuniqueness of Calabi-Yau metrics with maximal volume growth. https://arxiv.org/abs/2206.08210

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