We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in R. Besides identifying a condition on the structure of the domain which ensures the… (More)

We discuss a monotone quantity related to Huisken’s monotonicity formula and some technical consequences for mean curvature flow. CONTENTS 1. Maximizing Huisken’s Monotonicity Formula 1 2.… (More)

We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists… (More)