论文标题
$ \ mathbb {r}^{4} $中的最小分段线性锥
Minimal Piecewise Linear Cones in $\mathbb{R}^{4}$
论文作者
论文摘要
我们考虑$ \ mathbb {r}^4 $中的三维分段线性锥，它们是质量最小化W.R.T. Lipschitz绘制\ cite {almgren1976的含义，如\ cite {taylor76}所示。通过服用$ \ mathbb {r} $具有较低维度的$ \ mathbb {r} $的产物自然出现三个，而早期的文献证明了两个具有0维奇异性的存在。我们对所有可能的候选人进行了分类，并证明没有P.L.这五个之外的最小化器。
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.
