Browsing by Author "Osgood, Brad"
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- ItemA NOTE ON CONVEX CONFORMAL MAPPINGS(2019) Chuaqui Farrú, Martín Skandar; Osgood, Brad
- ItemAhlfors-Weill extensions for a class of minimal surfaces(2010) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad
- ItemBest Möbius Approximations of Convex and Concave Mappings(2023) Chuaqui, Martin; Osgood, BradWe study the best Mobius approximations (BMA) to convex and concave conformal mappings of the disk, including the special case of mappings onto convex polygons. The crucial factor is the location of the poles of the BMAs. Finer details are possible in the case of polygons through special properties of Blaschke products and the prevertices of the mapping function.
- ItemConcave conformal mappings and pre-vertices of Schwarz-Christoffel mappings(2012) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad
- ItemEllipses, near ellipses, and harmonic Möbius transformations.(2005) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad
- ItemFunctions with prescribed quasisymmetry quotients(1997) Chuaqui Farrú, Martín Skandar; Osgood, Brad; Stowe, D.
- ItemInjectivity criteria for holomorphic curves in Cn.(2009) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad
- ItemOn convolution, convex, and starlike mappings(2022) Chuaqui, Martin; Osgood, BradLet C and S* stand for the classes of convex and starlike mapping in D, and let <(co(C))over bar>, <(co(S*))over bar> denote the closures of the respective convex hulls. We derive characterizations for when the convolution of mappings in <(co(C))over bar> is convex, as well as when the convolution of mappings in <(co(S*))over bar> is starlike. Several characterizations in terms of convolution are given for convexity within <(co(C))over bar> and for starlikeness within <(co(S*))over bar>. We also obtain a correspondence via convolution between C and S*, as well as correspondences between the subclasses of convex and starlike mappings that have n-fold symmetry.
- ItemOSCILLATION OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS(CAMBRIDGE UNIV PRESS, 2009) Chuaqui, Martin; Duren, Peter; Osgood, Brad; Stowe, DennisIn this note we study the zeros of solutions of differential equations of the form u '' + pu = 0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are given.
- ItemQuasiconformal extensions to space of Weierstrass-Enneper lifts.(2014) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad
- ItemSchwarzian derivative criteria for valence of analytic and harmonic mappings(2007) Chuaqui, Martin; Duren, Peter; Osgood, BradFor analytic functions in the unit disk, general bounds on the Schwarzian derivative in terms of Nehari functions are shown to imply uniform local univalence and in some cases finite and bounded valence. Similar results are obtained for the Weierstrass-Enneper lifts of planar harmonic mappings to their associated minimal surfaces. Finally, certain classes of harmonic mappings are shown to have finite Schwarzian norm.
- ItemSchwarzian derivative criteria for valence of analytic and harmonic mappings.(2007) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad
- ItemSchwarzian derivatives and uniform local univalence.(2007) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad
- ItemSCHWARZIAN DERIVATIVES OF CONVEX MAPPINGS(SUOMALAINEN TIEDEAKATEMIA, 2011) Chuaqui, Martin; Duren, Peter; Osgood, BradA simple proof is given for Nehari's theorem that an analytic function f which maps the unit disk onto a convex region has Schwarzian norm parallel to f parallel to <= 2. The inequality in sharper form leads to the conclusion that no convex mapping with parallel to f parallel to = 2 can map onto a quasidisk. In particular, every bounded convex mapping has Schwarzian norm parallel to f parallel to < 2. The analysis involves a structural formula for the pre-Schwarzian of a convex mapping, which is studied in further detail.
- ItemSCHWARZIAN NORMS AND TWO-POINT DISTORTION(2011) Chuaqui, Martin; Duren, Peter; Ma, William; Mejia, Diego; Minda, David; Osgood, BradAn analytic function f with Schwarzian norm parallel to gf parallel to <= 2(1 + delta(2)) is shown to satisfy a pair of two-point distortion conditions, one giving a lower bound and the other an upper bound for the deviation. Conversely, each of these conditions is found to imply that parallel to gf parallel to <= 2(1 + delta(2)). Analogues of the lower bound are also developed for curves in R-n and for canonical lifts of harmonic mappings to minimal surfaces.
- ItemTWO-POINT DISTORTION THEOREMS FOR HARMONIC MAPPINGS(2009) Chuaqui, Martin; Duren, Peter; Osgood, BradIn earlier work, the authors have extended Nehari's well-known Schwarzian derivative criterion for univalence of analytic functions to a univalence criterion for canonical lifts of harmonic mappings to minimal surfaces. The present paper develops some quantitative versions of that result in the form of two-point distortion theorems. Along the way some distortion theorems for curves in R(n) are given, thereby recasting a recent injectivity criterion of Chuaqui and Gevirtz in quantitative form.
- ItemTwo-point distortion theorems for harmonic mappings.(2009) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad
- ItemUnivalence criteria for lifts of harmonic mappings to minimal surfaces.(2007) Chuaqui Farrú, Martín Skandar; Duren, Peter L., 1935-; Osgood, Brad