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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