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arXiv · 2208.05098

No semistability at infinity for Calabi-Yau metrics asymptotic to cones

Song Sun·Junsheng Zhang
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Abstract

We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of K\"ahler-Einstein metrics. A byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds, which bridges the gap between the general theory of Colding-Minicozzi and the classification results of Conlon-Hein.

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Song Sun, Junsheng Zhang. 2022-08-10. No semistability at infinity for Calabi-Yau metrics asymptotic to cones. https://doi.org/10.1007/s00222-023-01187-4

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