Expanding anisotropic network flow from three or four half-lines meeting in one point

In this paper, we prove in a first step for a smooth and elliptic anisotropy existence of an expanding regular network under anisotropic curvature flow with initial value given by three different half-lines starting in the same point. To achieve this, we adapt an analogous result from [O. C. Schnürer and F. Schulze, Self-similarly expanding networks to curve shortening flow, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), 4, 511–528] in the isotropic case. In a second step, we extend the existence result with similar methods to the situation where the initial value consists of four different half-lines starting from the same point.