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math.CV2017★ 4 cited
Quasiconformal extensions, Loewner chains, and the lambda-Lemma
Pavel Gumenyuk, István Prause
In 1972, J. Becker [J. Reine Angew. Math. 255] discovered a sufficient condition for quasiconformal extendibility of Loewner chains. Many known conditions for quasiconformal extend…
math.CV2017
Value regions of univalent self-maps with two boundary fixed points
Pavel Gumenyuk, Dmitri Prokhorov
In this paper we find the exact value region of the point evaluation functional over the class of all holomorphic injective self-maps $f:\math…
math.CV2017
Parametric representations and boundary fixed points of univalent self-maps of the unit disk
Pavel Gumenyuk
A classical result in the theory of Loewner's parametric representation states that the semigroup of all conformal self-maps of the unit disk norma…