Higher regularity for singular Kähler-Einstein metrics

Shih-Kai Chiu (University of Oxford)

Monday 22nd May, 2023 16:00-17:00 Maths 311B

Abstract

In a groundbreaking work, S. Donaldson and S. Sun show that the Gromov-Hausdorff limit of a sequence of polarized Kähler-Einstein manifolds is homeomorphic to a normal projective variety. This normal projective variety also admits a limiting Kähler-Einstein metric. Thanks to the work of C. Li, X. Wang, and C. Xu, the rough metric information near a singular point, i.e. the metric tangent cone, is entirely determined by the germ of the singularity. For geometric application, it is important to have a more refined understanding of the metric behavior near the singular points. In this talk, I will explain joint work with Gábor Székelyhidi on obtaining higher order regularity for such singular Kähler-Einstein metrics, generalizing an important work of H.-J. Hein and S. Sun.

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