Connected perimeter of planar sets
Functional Analysis
2020-05-27 v3
Abstract
We introduce a notion of connected perimeter for planar sets defined as the lower semi-continuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is also studied. We prove a representation formula which links the connected perimeter, the classical perimeter, and the length of suitable Steiner trees. We also discuss the application of this notion to the existence of solutions to a nonlocal minimization problem.
Cite
@article{arxiv.1906.09814,
title = {Connected perimeter of planar sets},
author = {François Dayrens and Simon Masnou and Matteo Novaga and Marco Pozzetta},
journal= {arXiv preprint arXiv:1906.09814},
year = {2020}
}
Comments
Advances in Calculus of Variations, In press