On Boundaries of $\varepsilon$-neighbourhoods of Planar Sets, Part I: Singularities

Autor:	Lamb, Jeroen S. W., Rasmussen, Martin, Timperi, Kalle
Rok vydání:	2020
Předmět:	Mathematics - Metric Geometry Mathematics - General Topology 51F30 (Primary) 57K20 54C50 51M15 58C06 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We study geometric and topological properties of singularities on the boundaries of $\varepsilon$-neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 : \textrm{dist}(x, E) \leq \varepsilon \}$ of planar sets $E \subset \mathbb{R}^2$. We develop a novel technique for analysing the boundary and obtain, for a compact set $E$ and $\varepsilon > 0$, a classification of singularities (i.e. non-smooth points) on $\partial E_\varepsilon$ into eight categories. We also show that the set of singularities is either countable or the disjoint union of a countable set and a closed, totally disconnected, nowhere dense set. Comment: 40 pages, 9 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.13515 Zobrazit plný text záznamu View this record from Arxiv