GTA Seminar: Wheeler -- The Willmore Flow in Riemannian Spaces

Speaker: Dr. Glen Wheeler (Wollongong)

https://sites.google.com/site/glenwheelermathman/

Time: **Tuesday**, May 28, 12NOON--1PM

Room: Carslaw 707A

Lunch: after the talk. The reservation at Law Annex 
Cafe is at 1:10PM. 

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Title: The Willmore Flow in Riemannian Spaces

Abstract: in this talk I will detail recent developments 
on the Willmore flow of surfaces in 3-manifolds with a 
prescribed Riemannian structure. If this structure is 
flat then local parabolic regularity for data in terms 
of the local L^2-norm of the second fundamental form is 
contained in Kuwert and Schaetzle's previous work on the 
Willmore functional. If there is some ambient curvature 
then several problems arise: the evolution of key 
geometric quantities becomes more complex and tools such 
as the Sobolev inequality are either invalid or hold only 
in special circumstances. Using a new concentration of 
area method we are able to recover an analogue of Kuwert 
and Schaetzle's local parabolic regularity theorem. We 
present one application yielding a global existence 
result in certain ambient spaces. This is joint work 
with Jan Metzger and Valentina-Mira Wheeler.
 
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Seminar website:

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