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arXiv · 2306.16941

A fractional Willmore-type energy functional -- subcritical observations

Simon Blatt·Giovanni Giacomin·Julian Scheuer·Armin Schikorra
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Abstract

We investigate surfaces with bounded L^p-norm of the fractional mean curvature, a quantity we shall refer to as fractional Willmore-type functional. In the subcritical case and under convexity assumptions we show how this Willmore-functional controls local parametrization, and conclude as consequences lower Ahlfors-regularity, a weak Michael-Simon type inequality, and an application to stability.

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Simon Blatt, Giovanni Giacomin, Julian Scheuer, Armin Schikorra. 2023-06-29. A fractional Willmore-type energy functional -- subcritical observations. https://arxiv.org/abs/2306.16941

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