Abstract: We construct Kahler-Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2 or if the singularity is smoothable. In complex dimension 2, we show that any complete Kahler-Einstein metric of negative scalar curvature near an isolated log canonical (non-log terminal) singularity is smoothly asymptotically close to one of the model metrics constructed by Kobayashi and Nakamura arising from hyperbolic geometry. If time permits, optimal asymptotics on hyperbolic cusps will also be discussed. This talk is based on joint work with Ved Datar, Hans-Joachim Hein, Jiang Xumin and Jian Song.
Speaker: Xin Fu is currently a visiting assistant professor at University of California, Irvine. He obtained his PhD degree from Rutgers University in 2020 under the supervison of professor Jian Song. His current research interest lies in complex geometry.
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