Sufficiently rich families of planar rings.
Supercomplex structures, surface soliton equations, and quasiconformal mappings
Hurwitz pairs and triples are discussed in connection with algebra, complex analysis, and field theory. The following results are obtained: (i) A field operator of Dirac type, which is called a Hurwitz operator, is introduced by use of a Hurwitz pair and its characterization is given (Theorem 1). (ii) A field equation of the elliptic Neveu-Schwarz model of superstring theory is obtained from the Hurwitz pair (⁴,³) (Theorem 2), and its counterpart connected with the Hurwitz triple is mentioned....
Teichmüller spaces and BMOA.
Teichmüller spaces are not starlike.
The angular distribution of mass by Bergman functions.
Let D = {z: |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For ε > 0 we define Σε = {z: |arg z| < ε}. We prove that for every ε > 0 there exists a δ > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0 thenThis problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatation for quasiconformal homeomorphisms of D.
The coefficients of quasiconformality of tori in n-space.
The extremum problem for analytic functions with finite area integral.
The generalized Neumann-Poincaré operator and its spectrum [Book]
The harmonic and quasiconformal extension operators
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.
The hyperbolic Gauss map and quasiconformal reflections.
The mapping by heights for quadratic differentials in the disk.
The Schwarzian derivative and conformally natural quasiconformal extensions from one to two to three dimensions.
The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle
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 is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest positive eigenvalue...
The space of quasisymmetric mappings.
The Unique Extremal QC Mapping and Uniqueness of Hahn-Banach Extensions
The weighted BMO condition and a constructive description of classes of analytic functions satisfying this condition.
Three functionals of a quasicircle. (Drei Funktionale eines Quasikreises.)
Two problems on doubling measures.
Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?
Typically real logharmonic mappings.
Über die Lösungsstruktur einer Differentialgleichung in der konformen Abbildung.