论文标题
无穷大对Calabi-yau指标渐近性均无可准性
No semistability at infinity for Calabi-Yau metrics asymptotic to cones
论文作者
论文摘要
我们通过消除唐纳森（Donaldson）和第一作者在2步变性理论中消除了中间K-序列锥的可能出现，从而发现了针对锥体渐近渐近的完全Calabi-yau指标渐近级的“无符号性”现象。这与Kähler-Einstein指标的局部奇异性的环境形成鲜明对比。证明的副产品是与渐近锥的多项式收敛速率，用于这种歧管，它弥合了冷 - 微浴的一般理论与康龙 - 海因的分类结果之间的差距。
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 Kähler-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.
