JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CARATHÉODORY FINITELY COMPACTNESS OF THE BOUNDED ATTRACTING BASIN OF THE ORIGIN
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • 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;
  PDF(new window)
 Abstract
We prove that the bounded attracting basin of the origin for a complex homogeneous polynomial of degree larger than two is Carathodory finitely compact.
 Keywords
balanced domain;Carathodory 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 crossref(new window)

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

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)