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