A fractional Willmore-type energy functional -- subcritical observations

Simon Blatt; Giovanni Giacomin; Julian Scheuer; Armin Schikorra

A fractional Willmore-type energy functional -- subcritical observations

Simon Blatt, Giovanni Giacomin, Julian Scheuer, Armin Schikorra

Mathematics

Research output: Working paper/Preprint › Preprint

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.

Original language	English
Publication status	Published - 29 Jun 2023

Keywords

math.AP
math.DG

Fields of Science and Technology Classification 2012

101 Mathematics

Cite this

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AU - Giacomin, Giovanni

AU - Scheuer, Julian

AU - Schikorra, Armin

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AB - 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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KW - math.DG

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BT - A fractional Willmore-type energy functional -- subcritical observations

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