Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 332, Issue 2, Pages 1189-1194Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2006.10.086
Keywords
harmonic mapping; univalent; linearly connected domain; second complex dilatation
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We investigate the relationship between the univalence of f and of h in the decomposition f = h + (g) over bar of a serise-preserving harmonic mapping defined in the unit disk D subset of C. Among other results, we determine the holomorphic univalent maps It for which there exists c > 0 such that every harmonic mapping of the form f = h + (g) over bar with vertical bar g'vertical bar < c vertical bar h'vertical bar is univalent. The notion of a linearly connected domain appears in our study in a relevant way. (c) 2006 Elsevier Inc. All rights reserved.
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