[CvGmt News] GFO-Pisa Seminars - Tuesday/Wednesday 26/27 May 2009

Carlo Mantegazza c.mantegazza at sns.it
Mon May 25 17:24:16 CEST 2009


Talk of Chau Wu, Tuesday 26/5/09 at 18.00 in Aula Dini,
Palazzo del Castelletto, Scuola Normale Superiore

Talk of Esther Cabezas-Rivas, Wednesday 27/5/09 at 18.00 in Aula Dini,
Palazzo del Castelletto, Scuola Normale Superiore

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26 May 2009 - Chao Wu
Department of Mathematics, Zhejiang University, China

On asymptotic behavior for singularities of the powers of mean curvature 
flow

Abstract: We consider the flow of a closed immersed hypersurface evolving 
along its normal direction with speed H^k, where H is the mean curvature 
and k is a positive constant. It is a natural generalization of the well 
known mean curvature flow. For a convex initial hypersurface, such flow 
will develop singularities after finite time, which can be classified as 
two types according to the blow up rate. We study the structure of the 
rescaled limits, and we show that for a Type I singularity, the limiting 
hypersurface satisfies an elliptic equation, for a Type II singularity, 
the limiting hypersurface must be a translating soliton.
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27 May 2009 - Esther Cabezas-Rivas
Mathematics Institute, University of Warwick

Ricci solitons on space-time

Abstract: In this talk, we will describe how the theory of optimal 
transportation can lead to new Ricci flow results independent of optimal 
transportation itself. In particular, given a Ricci flow on a manifold M 
over a time interval I, we introduce a second time parameter, and define 
natural gradient Ricci solitons on the space-time M x I. We show how part 
of the existing theory of Ricci flow is encoded in our solitons, and 
explain the link between this geometric construction and optimal 
transportation.
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