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arXiv · 2610.29891

On complete Ricci--flat Kähler manifolds

Song Sun·Junsheng Zhang
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Abstract

We study complete noncompact Ricci-flat Kähler manifolds. In the case of Euclidean volume growth, we prove that the underlying complex manifold is naturally quasi-projective and that the asymptotic cone is unique. Moreover, we establish no semistability at infinity and prove convergence to the asymptotic cone at a polynomial rate. In the case of sub-Euclidean volume growth, we construct complete Ricci-flat Kähler threefolds with bounded sectional curvature and finite topological type that admit no Kähler compactification.

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Song Sun, Junsheng Zhang. 2026-10-21. On complete Ricci--flat Kähler manifolds. https://arxiv.org/abs/2610.29891

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