FIC-UAI Publication Database -- Query Results

Arbelaez, H., Hernandez, R., & Sierra, W. (2022). Lower and upper order of harmonic mappings. J. Math. Anal. Appl., 507(2), 125837. Abstract: In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in D. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory. (C) 2021 Elsevier Inc. All rights reserved. Keywords: Harmonic mapping; Lower order; Upper order; Concave functions; Linearly connected domain; Schwarzian derivative show.php?record=1557
Chuaqui, M., & Hernandez, R. (2007). Univalent harmonic mappings and linearly connected domains. J. Math. Anal. Appl., 332(2), 1189–1194. Abstract: 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. Keywords: harmonic mapping; univalent; linearly connected domain; second complex dilatation show.php?record=42

Abstract: In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in D. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory. (C) 2021 Elsevier Inc. All rights reserved.

Keywords: Harmonic mapping; Lower order; Upper order; Concave functions; Linearly connected domain; Schwarzian derivative

show.php?record=1557

Abstract: 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.