Radii of covering disks for locally univalent harmonic mappings
Article Type
Research Article
Publication Title
Monatshefte fur Mathematik
Abstract
For a univalent smooth mapping f of the unit disk D of complex plane onto the manifold f(D) , let df(z0) be the radius of the largest univalent disk on the manifold f(D) centered at f(z0) (| z0| < 1). The main aim of the present article is to investigate how the radius dh(z0) varies when the analytic function h is replaced by a sense-preserving harmonic function f= h+ g¯. The main result includes sharp upper and lower bounds for the quotient df(z0) / dh(z0) , especially, for a family of locally univalent Q-quasiconformal harmonic mappings f= h+ g¯ on | z| < 1. In addition, estimate on the radius of the disk of convexity of functions belonging to certain linear invariant families of locally univalent Q-quasiconformal harmonic mappings of order α is obtained.
First Page
527
Last Page
548
DOI
10.1007/s00605-016-0904-2
Publication Date
7-1-2016
Recommended Citation
Graf, Sergey Yu; Ponnusamy, Saminathan; and Starkov, Victor V., "Radii of covering disks for locally univalent harmonic mappings" (2016). Journal Articles. 4399.
https://digitalcommons.isical.ac.in/journal-articles/4399
