JournalsrmiVol. 28, No. 1pp. 179–200

Tree-like decompositions of simply connected domains

  • Christopher J. Bishop

    SUNY at Stony Brook, USA
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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.

Cite this article

Christopher J. Bishop, Tree-like decompositions of simply connected domains. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 179–200

DOI 10.4171/RMI/673