Singular quasiregular mappings
Singular values, Ramanujan modular equations, and Landen transformations
A new connection between geometric function theory and number theory is derived from Ramanujan’s work on modular equations. This connection involves the function recurrent in the theory of plane quasiconformal maps. Ramanujan’s modular identities yield numerous new functional identities for for various primes p.
Solutions de l'équation de Beltrami
Some continuum phenomena and quasiconformal mappings
Some differential operators connected with quasiconformal deformations on manifold
Some homeomorphisms of the sphere conformal off a curve.
Some inequalities for the Hersch-Pfluger distortion function.
Some remarks on the Beltrami equation.
Stability in the Cauchy and Morera theorems for holomorphic functions and their spatial analogs.
Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues
The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = z: |z| > 1 can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely,...
Submultiplicative properties of the -distortion function
Some inequalities related to the submultiplicative properties of the distortion function are derived.
Subordination Chains and Univalence of Holomorphic Mappings in Cn.
Substantial boundary points for plane domains and Gardiner's conjecture.
Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself
In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.
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....