Tree-like decompositions of simply connected domains

Christopher J. Bishop

doi:10.4171/rmi/673

Tree-like decompositions of simply connected domains

Christopher J. Bishop

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We show that any simply connected rectifiable domain Ω can be decomposed into Lipschitz crescents using only crosscuts of the domain and using total length bounded by a multiple of the length of ∂Ω. In particular, this gives a new proof of a theorem of Peter Jones that such a domain can be decomposed into Lipschitz domains.

Original language	English
Pages (from-to)	179-200
Number of pages	22
Journal	Revista Matematica Iberoamericana
Volume	28
Issue number	1
DOIs	https://doi.org/10.4171/rmi/673
State	Published - 2012

Keywords

Crosscuts
Domain decomposition
Lipschitz domains
Medial axis
Spanners
Traveling salesman
Treelike decomposition

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10.4171/rmi/673

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AB - We show that any simply connected rectifiable domain Ω can be decomposed into Lipschitz crescents using only crosscuts of the domain and using total length bounded by a multiple of the length of ∂Ω. In particular, this gives a new proof of a theorem of Peter Jones that such a domain can be decomposed into Lipschitz domains.

KW - Crosscuts

KW - Domain decomposition

KW - Lipschitz domains

KW - Medial axis

KW - Spanners

KW - Traveling salesman

KW - Treelike decomposition

UR - https://www.scopus.com/pages/publications/84876814576

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DO - 10.4171/rmi/673

M3 - Article

AN - SCOPUS:84876814576

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EP - 200

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 1

ER -

Tree-like decompositions of simply connected domains

Abstract

Keywords

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