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CATEGORIES:Partial Differential Equations seminar
SUMMARY:A Li-Yau type inequality for free boundary surface
s with respect to the unit ball - Alexander Volkma
nn (Albert Einstein Institut\, Postdam)
DTSTART;TZID=Europe/London:20131104T150000
DTEND;TZID=Europe/London:20131104T160000
UID:TALK47747AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/47747
DESCRIPTION:A classical inequality due to Li and Yau states th
at for a closed immersed surface the Willmore ener
gy can be bounded from below by $4 \\pi$ times the
maximum multiplicity of the surface. Subsequently
\, Leon Simon proved a monotonicity identity for c
losed immersed surfaces\, which as a corollary lea
d to a new proof of the Li-Yau inequality. In this
talk we consider compact free boundary surfaces w
ith respect to the unit ball in $\\mathbb R^n^$\,\
n i.e. compact surfaces in $\\mathbb R^n$\, the bo
undaries of which meet the boundary of the unit ba
ll orthogonally. Inspired by Simon's idea we prove
a monotonicity identity in this setting. As a cor
ollary we obtain a Li-Yau type inequality\, which
can be seen as a generalization of an inequality d
ue to Fraser and Schoen to not necessarily minimal
surfaces. Using a similar idea Simon Brendle had
already extended\nFraser-Schoen's inequality to hi
gher dimensional minimal surfaces in all codimensi
ons.\n\n\n
LOCATION:CMS\, MR13
CONTACT:Prof. ClĂ©ment Mouhot
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