A fractional Willmore-type energy functional -- subcritical observations
Analysis of PDEs
2025-12-16 v1 Differential Geometry
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.
Cite
@article{arxiv.2306.16941,
title = {A fractional Willmore-type energy functional -- subcritical observations},
author = {Simon Blatt and Giovanni Giacomin and Julian Scheuer and Armin Schikorra},
journal= {arXiv preprint arXiv:2306.16941},
year = {2025}
}