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

• 成果类型: Article
• 署名作者: Sun, Song; Zhang, Junsheng
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01187-4
• 发表日期: 2023
• 页码: 461-494
• 关键词: gromov-hausdorff limits; kahler-manifolds; CONVERGENCE

摘要

We discover a no semistability at infinity phenomenon for complete Calabi-Yau metrics asymptotic to cones, which is proved 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 Kahler-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.