2 citations · 5 across the 5 of their papers we have counts for
7 papers
Sharp bounds for the growth and distortion of the analytic part of convex harmonic functions
María J. Martín
We obtain the sharp upper and lower bounds for the growth and distortion of the analytic parts of orientation-preserving harmonic mappings (normalized in the…
Continuous deformations of harmonic maps and their unitons
Alexandru Aleman, María J. Martín, Anna-Maria Persson +1
We consider harmonic maps on simply connected Riemann surfaces into the group of unitary matrices of order . It is known that a harmonic map with an associated a…
Criteria for bounded valence of harmonic mappings
Juha-Matti Huusko, María J. Martín
In 1984, Gehring and Pommerenke proved that if the Schwarzian derivative of a locally univalent analytic function in the unit disk satisfies that $\limsup_{|z|\to 1} |S(…
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…
A harmonic maps approach to fluid flows
Olivia Constantin, María Martín
We obtain a complete solution to the problem of classifying all two-dimensional ideal fluid flows with harmonic Lagrangian labelling maps; thus, we explicitly provide all solutions…
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…