Dimensions, Whitney covers, and tubular neighborhoods

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.

19 pages. Some minor corrections and updated references in this version

References in corpus (2)

• Packing dimension and Ahlfors regularity of porous sets in metric spaces
• Local multifractal analysis in metric spaces

Cited by in corpus (31)

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• Quasi-Assouad dimensions for random measures supported on $[0,1{]}^d$
• Local behavior of positive solutions of higher order conformally invariant equations with a singular set
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