A Li-Yau type inequality for free boundary surfaces with respect to the unit ball

Add to your list(s) Download to your calendar using vCal

• Alexander Volkmann (Albert Einstein Institut, Postdam)
• Monday 04 November 2013, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Prof. Clément Mouhot.

A classical inequality due to Li and Yau states that for a closed immersed surface the Willmore energy can be bounded from below by $4 \pi$ times the maximum multiplicity of the surface. Subsequently, Leon Simon 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 $\mathbb Rⁿ$, i.e. compact surfaces in $\mathbb R^n$, the boundaries of which meet the boundary of the unit ball orthogonally. Inspired by Simon’s idea we prove a monotonicity identity in this setting. As a corollary we obtain a Li-Yau type inequality, which can be seen as a generalization of an inequality due to Fraser and Schoen to not necessarily minimal surfaces. Using a similar idea Simon Brendle had already extended Fraser-Schoen’s inequality to higher dimensional minimal surfaces in all codimensions.

This talk is part of the Partial Differential Equations seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• CMS, MR13
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• My seminars
• Partial Differential Equations seminar
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.