Dimensions, Whitney covers, and tubular neighborhoods - UTU Research Portal

A1 Refereed original research article in a scientific journal

Dimensions, Whitney covers, and tubular neighborhoods

Authors: Antti Käenmäki, Juha Lehrbäck, Matti Vuorinen

Publisher: Department of Mathematics, Indiana University

Publication year: 2013

Journal: Indiana University Mathematics Journal

Journal name in source: Indiana University Mathematics Journal

Number in series: 6

Volume: 62

Issue: 6

First page : 1861

Last page: 1889

Number of pages: 29

ISSN: 0022-2518

DOI: https://doi.org/10.1512/iumj.2013.62.5155

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. © Indiana University Mathematics Journal.