A LiYau type inequality for free boundary surfaces with respect to the unit ball
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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 LiYau inequality. In this talk we consider compact free boundary surfaces with respect to the unit ball in $\mathbb R^{n}$,
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 LiYau 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
FraserSchoen’s inequality to higher dimensional minimal surfaces in all codimensions.
This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.
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