Revista Matemática Iberoamericana
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Published online: 2012-01-20
Tree-like decompositions of simply connected domainsChristopher J. Bishop (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. Iberoam. 28 (2012), 179-200. doi: 10.4171/RMI/673