# Anisotropic tubular neighborhoods in euclidean spaces

created by lussardi on 09 Apr 2018

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Submitted Paper

Inserted: 9 apr 2018
Last Updated: 9 apr 2018

Year: 2018

Abstract:

Let $E \subset \mathbb R^N$ be a compact set and $C\subset \mathbb R^N$ be a convex body with $0\in{\rm int}\,C$. We prove that the topological boundary of the anisotropic enlargement $E+rC$ is contained in a finite union of Lipschitz surfaces and we investigate the regularity of the volume function $V_E(r):= E+rC$ proving that up to a countable set $V_E$ is of class $C^1$.