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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