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We investigate surfaces with bounded Lp-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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A fractional Willmore-type energy functional−subcritical observations

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  • 发表日期：

    2025年

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  • Simon Blatt,
  • Giovanni Giacomin,
  • Armin Schikorra,
  • Julian Scheuer

摘要

We investigate surfaces with bounded Lp-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.