2 citations · 4 across the 8 of their papers we have counts for
10 papers
The Schwarzian derivative in several complex variables univalence and geometry
Rodrigo Hernández
In one complex variable the Schwarzian derivative characterizes the Möbius transformations, arises from a second-order linear equation, and controls univalence through the theorems…
Pre-Schwarzian derivative for Logharmonic mapppings
V. Bravo, R. Hernandez, O. Venegas
We introduce a new definition of pre-Schwarzian derivative for logharmonic mappings and basic properties such as the chain rule, multiplicative invariance and affine invariance are…
Normal harmonic mappings
Hugo Arbeláez, Rodrigo Hernández, Willy Sierra
The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk to the complex plane. In particular, w…
On weighted compositions preserving the Carathéodory class
Irina Arévalo, Rodrigo Hernández, María J. Martín +1
We characterize in various ways the weighted composition transformations which preserve the class of normalized analytic functions in the disk with positive real par…
On harmonic Bloch-type mappings
I. Efraimidis, J. Gaona, R. Hernández +1
Let be a complex-valued harmonic mapping defined in the unit disk . We introduce the following notion: we say that is a Bloch-type function if its Jacobian satis…
Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian DERIVATIVE
Rodrigo Hernández, María J. Martín
We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping in the unit disk is small enough, then is, indeed, globally univalent and…
Affine and linear invariant families of harmonic mappings
Martin Chuaqui, Rodrigo Hernández, María José Martín
We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk and determine the order of the family of mappings with bounded Schwarzian no…
Pre-Schwarzian and Schwarzian derivatives of harmonic mappings
Rodrigo Hernández, María J. Martín
In this paper we introduce a definition of the pre-Schwarzian and the Schwarzian derivatives of any locally univalent harmonic mapping in the complex plane without assuming any…
The order of a linearly invariant familiy in C^n
Martin Chuaqui, Rodrigo Hernandez
We study the (trace) norm of a linearly invariant family in the ball in $\C$. By adapting an approach that in one variable yields optimal results, we are able to derive an upper bo…
Harmonic Univalent Mappings and Linearly Connected Domains
M. Chuaqui, R. Hernandez
We investigate the relationship between the univalence of and of in the decomposition of a sense-preserving harmonic mapping defined in the unit disk $\mathbb…