A simply connected, homogeneous domain that is not a quasidisk.

Hjelle, Geir Arne

Displaying similar documents to “A simply connected, homogeneous domain that is not a quasidisk.”

Quasiconformal mappings onto John domains.

Juha Heinonen (1989)

Revista Matemática Iberoamericana

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In this paper we study quasiconformal homeomorphisms of the unit ball B = B = {x ∈ R: |x| < 1} of R onto John domains. We recall that John domains were introduced by F. John in his study of rigidity of local quasi-isometries [J]; the term John domain was coined by O. Martio and J. Sarvas seventeen years later [MS]. From the various equivalent characterizations we shall adapt the following definition based on diameter carrots, cf. [V4], [V5], [NV].

Concerning connectedness im kleinen and a related property

R. Moore (1922)

Fundamenta Mathematicae

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Sierpinski has shown (Wacław Sierpiński Sur une condition pour qu'un continu soit une courbe jordanienne, Fundamenta Mathematicae I (1920), pp. 44-60) that in order that a closed and connected set of points M should be a continuous curve it is necessary and sufficient that, for every positive number ϵ, the connected point-set M should be the sum of a finite number of closed and connected point-sets each of diameter less than ϵ. It follows that, as applied to point-sets which are closed,...

On the rectifiability of domains with finite perimeter

L. A. Caffarelli, N. M. Rivière (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On locally biholomorphic mappings from multi-connected onto simply connected domains

Piotr Liczberski, Victor V. Starkov (2005)

Annales Polonici Mathematici

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We continue E. Ligocka's investigations concerning the existence of m-valent locally biholomorphic mappings from multi-connected onto simply connected domains. We decrease the constant m, and also give the minimum of m in the case of mappings from a wide class of domains onto the complex plane ℂ.