CARATHÉODORY FINITELY COMPACTNESS OF THE BOUNDED ATTRACTING BASIN OF THE ORIGIN

• Journal title : Honam Mathematical Journal
• Volume 29, Issue 2,  2007, pp.299-305
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2007.29.2.299
Title & Authors
CARATHÉODORY FINITELY COMPACTNESS OF THE BOUNDED ATTRACTING BASIN OF THE ORIGIN
Park, Sung-Hee;

Abstract
We prove that the bounded attracting basin of the origin for a complex homogeneous polynomial of degree larger than two is Carath$\small{\$odory finitely compact.
Keywords
balanced domain;Carath$\small{\$odory finitely compact;basin of attraction;
Language
English
Cited by
References
1.
T. J. Barth, The Kobayashi indicatrix at the center of a circular domain, Proc. Amer. Math. Sco. 88 (1983) 527-530

2.
G. Berg, Hyperconvexity and the Caratheodory metric, Arch. Math. 32 (1979) 189-191

3.
P. Jakobczak & M. Jarnicki, Lectures on holomorphic functions of several complex variables, PS File at 'http://www.im.uj.edu.pl/-jarnicki/mjp.htm', 2001.

4.
M. Jarnicki & P. Pflug, A counterexample for Kobayashi completeness of balanced domains, Proc. Amer. Math. Soc. 112 (1991), 973-978.

5.
M. Jarnicki & P. Pflug, Invariant Distances and Metrics in Complex Analysis, de Gruyter Expositions in Mathematics 9, Walter de Gruyter 1993.

6.
M. Jarnicki, P. Pflug, & W. Zwonek On Bergman completeness of non- hyperconvex domains, Univ. lag. Acta Math. 38 (2000), 169-184.

7.
N. Kerzman & J.-P. Rosay, Fonctions plurisousharmoniques d'exhasution bornees et domaines taut, Math. Ann. 257 (1981), 171-184.

8.
V. Z. Khristov, A sufficient condition for Caratheodory finite compactness of bounded complete circular domain in \$C^{n}\$, C. R. Acad. Bulg. Sci. 42 (3) (1989), 9-11.

9.
S.-H. Park, Tautness and Kobayashi hyperbolciity, doctor theses, University of Oldenburg (2003).

10.
P. Pflug, Invariant metrics and completeness, J. Korean Math. Soc. 37 (2) (2000), 269-284.

11.
T. Ueda, Fatou sets in complex dynamics on projective spaces, J. Math. Soc. Japan 46 (1994), 545-555.