Displaying similar documents to “Dirichlet's Principle, Uniqueness of Harmonic Maps and Extremal QC Mappings”

The harmonic and quasiconformal extension operators

Dariusz Partyka, Ken Sakan, Józef Zając (1999)

Banach Center Publications

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Different aspects of the boundary value problem for quasiconformal mappings and Teichmüller spaces are expressed in a unified form by the use of the trace and extension operators. Moreover, some new results on harmonic and quasiconformal extensions are included.

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

The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle

Dariusz Partyka (1995)

Banach Center Publications

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This paper provides sufficient conditions on a quasisymmetric automorphism γ of the unit circle which guarantee the existence of the smallest positive eigenvalue of γ. They are expressed by means of a regular quasiconformal Teichmüller self-mapping φ of the unit disc Δ. In particular, the norm of the generalized harmonic conjugation operator A γ : ℍ → ℍ is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest...

Extremal plurisubharmonic functions

Urban Cegrell, Johan Thorbiörnson (1996)

Annales Polonici Mathematici

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We study different notions of extremal plurisubharmonic functions.

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.