Embedding univalent functions in filtering Loewner chains in higher dimension

Chordal Loewner families and univalent Cauchy transforms

We study chordal Loewner families in the upper half-plane and show that they have a parametric representation. We show one, that to every chordal Loewner family there corresponds a unique measurable family of probability measures on the real line, and two, that to every measurable family of probability measures on the real line there corresponds a unique chordal Loewner family. In both cases th...

Loewner Chains in the Unit Disk

In this paper we introduce a general version of the notion of Loewner chains which comes from the new and unified treatment, given in [5], of the radial and chordal variant of the Loewner differential equation, which is of special interest in geometric function theory as well as for various developments it has given rise to, including the famous Schramm-Loewner evolution. In this very general s...

Boundary behaviour of Loewner Chains

In paper found conditions that guarantee that solution of LoewnerKufarev equation maps unit disc onto domain with quasiconformal rectifiable boundary, or it has continuation on closed unit disc, or it’s inverse function has continuation on closure of domain.

Sufficient Inequalities for Univalent Functions

In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.

Univalent Functions with Univalent Derivatives. Ii