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比利时vs摩洛哥足彩 ,
university of california san diego

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differential geometry seminar

frederick fong

stanford university

collapsing behavior of the kahler-ricci flow and its singularity analysis.

abstract:

in this talk, i will discuss my recent works on the collapsing behavior of the kahler-ricci flow. the first work studies the kahler-ricci flow on $p^1$-bundles over kahler-einstein manifolds. we proved that if the initial kahler metric is constructed by the calabi's ansatz and is in the suitable kahler class, the flow must develop type i singularity and the singularity model is $p^1 x c^n$. it is an extension of song-weinkove's work on hirzebruch surfaces. the second work discusses the collapsing behavior in a more general setting without any symmetry assumption. we showed that if the limiting kahler class of the flow is given by a holomorphic submersion and the ricci curvature is uniformly bounded from above with respect to the initial metric, then the fibers will collapse in an optimal rate, i.e. diam $\sim (t-t)^{1/2}$. it gives a partial affirmative answer to a conjecture stated in song-szekelyhidi-weinkove's work on projective bundles.

host: ben weinkove

january 13, 2012

1:00 pm

ap&m 6402

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