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arXiv · 2606.13011

Complete Calabi-Yau metrics on noncompact K3 fibered threefolds

Ruiming Liang
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Abstract

In this article, we construct complete Calabi--Yau metrics on Lefschetz K3 fibrations over $\mathbb{C}$. Our approach involves a gluing construction for a collapsing approximate metric, followed by a perturbation argument. These Calabi--Yau metrics have linear volume growth, unbounded sectional curvature, and are Gromov--Hausdorff asymptotic to a product $\mathbb{R}\times Z$, where $Z$ is a compact singular metric space.

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Ruiming Liang. 2026-06-11. Complete Calabi-Yau metrics on noncompact K3 fibered threefolds. https://arxiv.org/abs/2606.13011

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