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The schoenflies extension in the analytic case

Research paper by William Huebsch, Marston Morse

Indexed on: 01 Dec '61Published on: 01 Dec '61Published in: Annali di Matematica Pura ed Applicata (1923 -)



Abstract

Let S be an (n−1)-sphere in a euclidean n-space E. Let B be the closed n-ball in E bounded by S. Let z be an arbitrary point of\(\mathop B\limits^ \circ \). A real analytic diffeomorphism f of S into E admits a homeomorphic extension F which is defined over some open neighborhood N of B and such that F | (N−z) is an analytic diffeomorphism. We give a new proof of this theorem to serve as a model for a forthcoming theory of analytic families of such extensions.