Displaying similar documents to “A distortion theorem for quasiconformal automorphisms of the unit disk”

Hilbert-Smith Conjecture for K - Quasiconformal Groups

Gong, Jianhua (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 30C60 A more general version of Hilbert's fifth problem, called the Hilbert-Smith conjecture, asserts that among all locally compact topological groups only Lie groups can act effectively on finite-dimensional manifolds. We give a solution of the Hilbert-Smith Conjecture for K - quasiconformal groups acting on domains in the extended n - dimensional Euclidean space.

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...

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.

Nonlinear analysis and quasiconformal mappings from the perspective of PDEs

Tadeusz Iwaniec (1999)

Banach Center Publications

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Contents Introduction 119 1. Quasiregular mappings 120 2. The Beltrami equation 121 3. The Beltrami-Dirac equation 122 4. A quest for compactness 124 5. Sharp L p -estimates versus variational integrals 125 6. Very weak solutions 128 7. Nonlinear commutators 129 8. Jacobians and wedge products 131 9. Degree formulas 134 References 136