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arXiv · 1209.0629

Dimensions, Whitney covers, and tubular neighborhoods

Antti Käenmäki·Juha Lehrbäck·Matti Vuorinen
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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.

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Antti Käenmäki, Juha Lehrbäck, Matti Vuorinen. 2014-05-14. Dimensions, Whitney covers, and tubular neighborhoods. https://doi.org/10.1512/iumj.2013.62.5155

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