On complete Calabi-Yau manifolds asymptotic to cones

Junsheng Zhang, University of California Berkeley

We proved a "no semistability at infinity" result 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-Sun. As a consequence, a classification result for complete Calabi-Yau manifolds with Euclidean volume growth and quadratic curvature decay is given. Moreover a byproduct of the proof is a polynomial convergence rate  to the asymptotic cone for such manifolds. Joint work with Song Sun.

QNC 2501