Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

On the theorem of Hayman and Wu

Author(s): S. Rohde
Journal: Proc. Amer. Math. Soc. 130 (2002), 387-394.
MSC (2000): Primary 30C35
Posted: September 19, 2001
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We show that the Hayman-Wu constant Øis strictly smaller than $4\pi.$Previously it has been shown that $\pi^2\leq$ Ø $ \leq 4\pi.$ A main tool in our proof is an analysis of the hyperbolic geodesic curvature of straight lines in simply connected domains.

References:

1.
B. Brown-Flinn, Hyperbolic convexity and level sets of analytic functions, Indiana Univ. Math. J. 32 (1983), 831-841. MR 85b:30010

2.
J. Fernández, J. Heinonen, O. Martio, Quasilines and conformal mappings, J. Analyse Math. 52 (1989), 117-132. MR 90a:30017

3.
J. Garnett, F. Gehring, P. Jones, Conformally invariant length sums, Indiana Univ. Math. J. 32 (1983), 809-829. MR 85a:30033

4.
J. Fernández, A. Granados, On geodesic curvature and conformal mapping, Algebra i Analiz 9 (1997), 220-244; translation in S. Petersburg Math. J. 9 (1998), 615-637. MR 98k:30010

5.
W. Hayman, J.-M. Wu, Level sets of univalent functions, Comment. Math. Helv. 56 (1981), 366-403. MR 83b:30008

6.
B. Osgood, Some properties of $f''/f'$ and the Poincaré metric, Indiana Univ. Math. J. 31 (1982), 449-461. MR 83j:30019

7.
K. Øyma, Harmonic measure and conformal length, Proc. Amer. Math. Soc. 115 (1992), 687-689. MR 92i:30007

8.
K. Øyma, The Hayman-Wu constant, Proc. Amer. Math. Soc. 119 (1993), 337-338. MR 93k:30031

9.
Chr. Pommerenke, Univalent functions, Vandenhoeck and Ruprecht (1975). MR 58:22526

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30C35

Retrieve articles in all Journals with MSC (2000): 30C35

Additional Information:

S. Rohde
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350

DOI: 10.1090/S0002-9939-01-06209-8
PII: S 0002-9939(01)06209-8
Received by editor(s): February 29, 2000
Posted: September 19, 2001
Additional Notes: Research supported by NSF grant DMS-9970398
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2001, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google