Shortest paths in arbitrary plane domains

DOI10.4153/S0008414X20000784zbMath1493.54036arXiv1903.06737OpenAlexW3100676098MaRDI QIDQ5075982

Lex G. Oversteegen, Logan C. Hoehn, Edward D. Tymchatyn

Publication date: 12 May 2022

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.06737

zbMATH Keywords

plane domainpathlengthhomotopyshortestanalytic covering map

Mathematics Subject Classification ID

Topological spaces of dimension (leq 1); curves, dendrites (54F50) Length, area and volume in real or complex geometry (51M25)

Cites Work

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• Shortest paths in simply connected regions in \({\mathbb{R}}^ 2\)
• One-dimensional sets and planar sets are aspherical
• Homotopy type of planar Peano continua
• A canonical parameterization of paths in $\mathbb{R}^n$
• Extension of isotopies in the plane
• Equicontinuity and n-Length
• A special parameterization of curves

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