Revista Matemática Iberoamericana


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Volume 28, Issue 1, 2012, pp. 179–200
DOI: 10.4171/RMI/673

Published online: 2012-01-20

Tree-like decompositions of simply connected domains

Christopher J. Bishop[1]

(1) SUNY at Stony Brook, USA

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.

Keywords: Domain decomposition, traveling salesman, medial axis, Lipschitz domains, spanners, crosscuts, treelike decomposition

Bishop Christopher: Tree-like decompositions of simply connected domains. Rev. Mat. Iberoamericana 28 (2012), 179-200. doi: 10.4171/RMI/673