Seminar: On complete Calabi-Yau metrics with Euclidean volume growth and quadratic curvature decay

Seminar| Institute of Mathematical Sciences

Abstract: We eliminate the possible appearance of an  intermediate  K-semistable cone in the 2-step degeneration theory developed by Donaldson-Sun. 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 Calabi-Yau manifolds asymptotic to cones, which bridges the gap between the general theory of Colding-Minicozzi and the classification results of Conlon-Hein. This is a joint work with Song Sun.