Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-01T03:54:20.395Z Has data issue: false hasContentIssue false
  • English
  • Français

THE MODULUS OF THE IMAGE ANNULI UNDER UNIVALENT HARMONIC MAPPINGS AND A CONJECTURE OF NITSCHE

Published online by Cambridge University Press:  30 October 2001

ABDALLAH LYZZAIK
ABDALLAH LYZZAIK
Affiliation:
Department of Mathematics, American University of Beirut, Beirut, Lebanon; [email protected]
Get access

Abstract

The object of the paper is to show that if f is a univalent, harmonic mapping of the annulus A(r, 1) = {z : r < [mid ]z[mid ] < 1} onto the annulus A(R, 1), and if s is the length of the segment of the Grötzsch ring domain associated with A(r, 1), then R < s. This gives the first, quantitative upper bound of R, which relates to a question of J. C. C. Nitsche that he raised in 1962. The question of whether this bound is sharp remains open.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 369 - 384
Copyright
The London Mathematical Society 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)