Displaying similar documents to “What is a disk?”

On bounded univalent functions that omit two given values

Dimitrios Betsakos (1999)

Colloquium Mathematicae

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Let a,b ∈ z: 0<|z|<1 and let S(a,b) be the class of all univalent functions f that map the unit disk into {a,bwith f(0)=0. We study the problem of maximizing |f’(0)| among all f ∈ S(a,b). Using the method of extremal metric we show that there exists a unique extremal function which maps onto a simply connnected domain D 0 bounded by the union of the closures of the critical trajectories of a certain quadratic differential. If a<0

Lebesgue measure and mappings of the Sobolev class W 1 , n

O. Martio (1995)

Banach Center Publications

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We present a survey of the Lusin condition (N) for W 1 , n -Sobolev mappings f : G → ℝ n defined in a domain G of ℝ n . Applications to the boundary behavior of conformal mappings are discussed.