Dimensions, Whitney covers, and tubular neighborhoods
Metric Geometry
2017-02-03 v3
Abstract
Working in doubling metric spaces, we examine the connections between different dimensions, Whitney covers, and geometrical properties of tubular neighborhoods. In the Euclidean space, we relate these concepts to the behavior of the surface area of the boundaries of parallel sets. In particular, we give characterizations for the Minkowski and the spherical dimensions by means of the Whitney ball count.
Keywords
Cite
@article{arxiv.1209.0629,
title = {Dimensions, Whitney covers, and tubular neighborhoods},
author = {Antti Käenmäki and Juha Lehrbäck and Matti Vuorinen},
journal= {arXiv preprint arXiv:1209.0629},
year = {2017}
}
Comments
19 pages. Some minor corrections and updated references in this version