A fractional Willmore-type energy functional -- subcritical observations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911316160020480 |
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| author | Blatt, Simon Giacomin, Giovanni Scheuer, Julian Schikorra, Armin |
| author_facet | Blatt, Simon Giacomin, Giovanni Scheuer, Julian Schikorra, Armin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16941 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A fractional Willmore-type energy functional -- subcritical observations Blatt, Simon Giacomin, Giovanni Scheuer, Julian Schikorra, Armin Analysis of PDEs Differential Geometry 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. |
| title | A fractional Willmore-type energy functional -- subcritical observations |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2306.16941 |