Fredholm spectrum and Grunsky inequalities in general domains
Gauss curvature estimates for minimal graphs
Generalized problem of starlikeness for products of close-to-star functions
We consider functions of the type , where are real numbers and are -strongly close-to-starlike functions of order . We look for conditions on the center and radius of the disk (a,r) = z:|z-a| < r, |a| < r ≤ 1 - |a|, ensuring that F((a,r)) is a domain starlike with respect to the origin.
Geometric characterization for affine mappings and Teichmüller mappings
We characterize affine mappings on the unit disk and on rectangles by module conditions. The main result generalizes the classic Schwarz lemma. As an application, we give a sufficient condition for a K-quasiconformal mapping on a Riemann surface to be a Teichmüller mapping.
Geometric characterization for homeomorphisms between disks
We give some characterizations for certain homeomorphisms between disks in the complex plane, and we prove some Schwarz type theorems for such homeomorphisms. Our results replace the main result of Chen [Studia Math. 157 (2003)] which we show to be false.
Grunsky coefficient inequalities, Caratheodory metric and extremal quasiconformal mappings.
Hardy norm, Bergman norm, and univalency
Harmonic mappings onto parallel slit domains
We consider typically real harmonic univalent functions in the unit disk 𝔻 whose range is the complex plane slit along infinite intervals on each of the lines x ± ib, b > 0. They are obtained via the shear construction of conformal mappings of 𝔻 onto the plane without two or four half-lines symmetric with respect to the real axis.
Inclusion and neighborhood properties of certain subclasses of analytic, multivalent functions of complex order involving convolution.
Inclusion relationships between classes of functions defined by subordination
The purpose of the present paper is to investigate various inclusion relationships between several classes of analytic functions defined by subordination. Many interesting applications involving the well-known classes of functions defined by linear operators are also considered.
Inequalities associating hypergeometric functions with planar harmonic mappings.
Integral Means and Radial Growth of Bloch Functions.
Level sets of univalent functions.
Linearly invariant families of holomorphic functions in the unit polydisc
In this paper we extend the definition of the linearly invariant family and the definition of the universal linearly invariant family to higher dimensional case. We characterize these classes and give some of their properties. We also give a relationship of these families with the Bloch space.
Locally biholomorphic mappings of multiconnected domains.
Locally isometric families of minimal surfaces.
Logarithmic coefficients of univalent functions.
Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen.
Löwnersche Differentialgleichung und Schlichtheitskriterien.