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A geometric inequality for convex free boundary hypersurfaces in the unit ball


Authors: Ben Lambert and Julian Scheuer
Journal: Proc. Amer. Math. Soc. 145 (2017), 4009-4020
MSC (2010): Primary 53C44, 58C35, 58J32
DOI: https://doi.org/10.1090/proc/13516
Published electronically: March 27, 2017
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Abstract: We use the inverse mean curvature flow with a free boundary perpendicular to the sphere to prove a geometric inequality involving the Willmore energy for convex hypersurfaces of dimension $ n\geq 3$ with boundary on the sphere.


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Additional Information

Ben Lambert
Affiliation: University of Konstanz, Zukunftskolleg, Box 216, 78457 Konstanz, Germany
Email: benjamin.lambert@uni-konstanz.de

Julian Scheuer
Affiliation: Albert-Ludwigs-Universität, Mathematisches Institut, Eckerstr. 1, 79104 Freiburg, Germany
Email: julian.scheuer@math.uni-freiburg.de

DOI: https://doi.org/10.1090/proc/13516
Keywords: Inverse mean curvature flow, Free boundary problem, Geometric inequality, Willmore functional
Received by editor(s): June 21, 2016
Received by editor(s) in revised form: September 27, 2016
Published electronically: March 27, 2017
Communicated by: Lei Ni
Article copyright: © Copyright 2017 American Mathematical Society

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