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arXiv · 2503.00649

$C^\infty$ rectifiability of stationary varifolds

Camillo Brena·Camillo De Lellis·Federico Franceschini
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Abstract

In this paper we prove that, for every integers $m\geq 2$ and $n\geq 1$, the support of any stationary $m$-dimensional integer rectifiable varifold $V$ in an open set $U\subset \mathbb R^{m+n}$ is $C^\infty$ rectifiable, namely it can be covered, up to an $H^m$-null set, with countably many $C^\infty$ $m$-dimensional graphs.

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Camillo Brena, Camillo De Lellis, Federico Franceschini. 2025-03-01. $C^\infty$ rectifiability of stationary varifolds. https://arxiv.org/abs/2503.00649

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