Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Distortion theorems for higher order Schwarzian derivatives of univalent functions

Author: Eric Schippers
Journal: Proc. Amer. Math. Soc. 128 (2000), 3241-3249
MSC (1991): Primary 30C55
Published electronically: April 28, 2000
MathSciNet review: 1706981
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


Let $\tilde{\mathcal{S}}$ denote the class of functions which are univalent and holomorphic on the unit disc. We derive a simple differential equation for the Loewner flow of the Schwarzian derivative of a given $f \in \tilde{\mathcal{S}}$. This is used to prove bounds on higher order Schwarzian derivatives which are sharp for the Koebe function. As well we prove some two-point distortion theorems for the higher order Schwarzians in terms of the hyperbolic metric.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C55

Retrieve articles in all journals with MSC (1991): 30C55

Additional Information

Eric Schippers
Affiliation: Department of Mathematics, University of Toronto, 100 St. George St., Toronto, Ontario, Canada M5S 3G3

PII: S 0002-9939(00)05623-9
Keywords: Schwarzian derivative, univalent functions, hyperbolic metric
Received by editor(s): December 14, 1998
Published electronically: April 28, 2000
Additional Notes: This paper is part of thesis work at the University of Toronto.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia