TY - JOUR
AU - Valfells, Asgeir
PY - 2024/02/26
Y2 - 2024/04/22
TI - Minimal piecewise linear cones in $\mathbb{R}^4$
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 130
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-140336
UR - https://www.mscand.dk/article/view/140336
SP -
AB - <p>We consider three dimensional piecewise linear cones in $\mathbb{R}^4$ that are mass minimal with respect to Lipschitz maps in the sense of [Almgren, F., Mem. Amer. Math. Soc. 4 (1976), no. 165] as in [Taylor, J. E., Ann. of Math. (2) 103 (1976), no. 3, 489–539]. 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 piecewise linear minimizers outside these five.</p>
ER -