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SUMMARY:A Li-Yau type inequality for free boundary surfaces with respect t
 o the unit ball - Alexander Volkmann (Albert Einstein Institut\, Postdam)
DTSTART:20131104T150000Z
DTEND:20131104T160000Z
UID:TALK47747@talks.cam.ac.uk
CONTACT:Prof. Clément Mouhot
DESCRIPTION:A classical inequality due to Li and Yau states that for a clo
 sed immersed surface the Willmore energy can be bounded from below by $4 \
 \pi$ times the maximum multiplicity of the surface. Subsequently\, Leon Si
 mon proved a monotonicity identity for closed immersed surfaces\, which as
  a corollary lead to a new proof of the Li-Yau inequality. In this talk we
  consider compact free boundary surfaces with respect to the unit ball in 
 $\\mathbb R^n^$\,\n i.e. compact surfaces in $\\mathbb R^n$\, the boundari
 es of which meet the boundary of the unit ball orthogonally. Inspired by S
 imon's idea we prove a monotonicity identity in this setting. As a corolla
 ry we obtain a Li-Yau type inequality\, which can be seen as a generalizat
 ion of an inequality due to Fraser and Schoen to not necessarily minimal s
 urfaces. Using a similar idea Simon Brendle had already extended\nFraser-S
 choen's inequality to higher dimensional minimal surfaces in all codimensi
 ons.\n\n\n
LOCATION:CMS\, MR13
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