SMS scnews item created by Zhou Zhang at Wed 22 May 2013 1623
Type: Seminar
Distribution: World
Expiry: 12 Jun 2013
Calendar1: 28 May 2013 1200-1300
CalLoc1: Carslaw 707A
Auth: zhangou@como.maths.usyd.edu.au

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

Speaker: Dr. Glen Wheeler (Wollongong)

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/


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