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arXiv · 2409.11861

A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by $C^{1,\alpha}$ Multiple Valued Functions

Nicolau S. Aiex
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Abstract

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.

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Nicolau S. Aiex. 2024-09-18. A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by $C^{1,\alpha}$ Multiple Valued Functions. https://arxiv.org/abs/2409.11861

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