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Department of Mathematics,
University of California San Diego

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Department of Mathematics Colloquium

Professor Xiaohua Zhu

Peking University

Limit and singularities of Kaehler-Ricci flow

Abstract:

As we know, Kaehler-Ricci flow can be reduced to solve a class of  parabolic   complex Monge-Amp\`ere equations for Kaehler potentials and  the solutions usually depend on the Kaehler class of initial metric.   Thus there  gives a  degeneration of Kaehler metrics arising from the Kaehler-Ricci flow.  For a class of $G$-spherical manifolds,   we can  use  the local estimate  of  Monge-Amp\`ere equations as well as  the H-invariant for $C^*$-degeneration  to determine the limit of  Kaehler-Ricci flow after resales.  In particular,  on such manifolds,  the flow will develop the singularities of  type II.  

Host: Lei Ni

January 16, 2025

4:00 PM

APM 6402

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