Sets resilient to erosion
Metric Geometry
2011-01-25 v1
Abstract
The erosion of a set in Euclidean space by a radius r>0 is the subset of X consisting of points at distance >/-r from the complement of X. A set is resilient to erosion if it is similar to its erosion by some positive radius. We give a somewhat surprising characterization of resilient sets, consisting in one part of simple geometric constraints on convex resilient sets, and, in another, a correspondence between nonconvex resilient sets and scale-invariant (e.g., 'exact fractal') sets.
Cite
@article{arxiv.1101.4416,
title = {Sets resilient to erosion},
author = {Wesley Pegden},
journal= {arXiv preprint arXiv:1101.4416},
year = {2011}
}
Comments
24 pages, 14 figures