A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by $C^{1,\alpha}$ Multiple Valued Functions
| Autor: | Aiex, Nicolau S. |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We provide a counter-example to Hutchinson's original proof of $C^{1,\alpha}$ 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. Comment: 16 pages, 2 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|