GTA Seminar : Wheeler -- Some Free Boundary Value Problems in Mean Curvature Flow and Fully Nonlinear Curvature Flows

Speaker: Dr. Valentina-Mira Wheeler (Wollongong)

https://ris.uow.edu.au/ris_public/WebObjects/RISPublic.woa/wa/Staff/selectPerson?id=84160&group=3944

Time: Tuesday, April 29, 12NOON--1PM. 

Room: Carslaw 535A. 

Lunch: seminar lunch is right after the talk. 

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Title: Some Free Boundary Value Problems in Mean Curvature Flow 
and Fully Nonlinear Curvature Flows
 
Abstract: in this talk we present an overview of the current research 
in mean curvature flow and fully nonlinear curvature flows with free 
boundaries, with particular focus on our own results. Firstly we 
consider the scenario of a mean curvature flow solution with a 
ninety-degree angle condition on a fixed hypersurface in Euclidean 
space, that we call  the contact hypersurface. We prove that under 
restrictions on either the initial hypersurface (such as rotational 
symmetry) or restrictions on the contact hypersurface the flow exists 
for all times and converges to a self-similar solution. We also discuss 
the possibility of a curvature singularity appearing on the free boundary 
contained in the contact hypersurface. We extend some of these results 
to the setting of a hypersurface evolving in its normal direction with 
speed given by a fully nonlinear functional of the principal curvatures.

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Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/