A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by $C^{1,α}$ Multiple Valued Functions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914951823622144 |
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| author | Aiex, Nicolau S. |
| author_facet | Aiex, Nicolau S. |
| contents | We provide a counter-example to Hutchinson's original proof of $C^{1,α}$ representation of curvature $m$-varifolds with $L^q$-integrable second fundamental form and $q>m$ in [6]. We also provide an alternative proof of the same result and introduce a method of decomposing varifolds into nested components preserving weakly differentiability of a given function. Furthermore, we prove the structure theorem for curvature varifolds with null second fundamental form which is widely used in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by $C^{1,α}$ Multiple Valued Functions Aiex, Nicolau S. Differential Geometry 28A75, 49Q20 We provide a counter-example to Hutchinson's original proof of $C^{1,α}$ representation of curvature $m$-varifolds with $L^q$-integrable second fundamental form and $q>m$ in [6]. We also provide an alternative proof of the same result and introduce a method of decomposing varifolds into nested components preserving weakly differentiability of a given function. Furthermore, we prove the structure theorem for curvature varifolds with null second fundamental form which is widely used in the literature. |
| title | A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by $C^{1,α}$ Multiple Valued Functions |
| topic | Differential Geometry 28A75, 49Q20 |
| url | https://arxiv.org/abs/2409.11861 |