Dimensions, Whitney covers, and tubular neighborhoods

Abstract

Working in doubling metric spaces, we examine the connections between\ndifferent dimensions, Whitney covers, and geometrical properties of tubular\nneighborhoods. In the Euclidean space, we relate these concepts to the behavior\nof the surface area of the boundaries of parallel sets. In particular, we give\ncharacterizations for the Minkowski and the spherical dimensions by means of\nthe Whitney ball count.\n