Minimal Piecewise Linear Cones in $\mathbb{R}^{4}$

Ásgeir Valfells

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arXiv · 2208.13718

Minimal Piecewise Linear Cones in $\mathbb{R}^{4}$

Ásgeir Valfells

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Abstract

We consider three dimensional piecewise linear cones in $\mathbb{R}^4$ that are mass minimizing w.r.t. Lipschitz maps in the sense of \cite{almgren1976existence} as in \cite{Taylor76}. There are three that arise naturally by taking products of $\mathbb{R}$ with lower dimensional cases and earlier literature has demonstrated the existence of two with 0-dimensional singularities. We classify all possible candidates and demonstrate that there are no p.l. minimizers outside these five.

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Ásgeir Valfells. 2022-08-29. Minimal Piecewise Linear Cones in $\mathbb{R}^{4}$. https://arxiv.org/abs/2208.13718

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