Transfer of Estimates from Convex to Strongly Pseudoconvex Domains in $ℂ^N$

ArticleOriginal scientific text

Title

Authors ¹

In this article, estimates of the hyperbolic and Carathéodory distances in domains

G \subset \subset ℂ^{n}

, n ≥ 1, are obtained. They are equally valid for the Kobayashi distance.

M. Abate, Iteration theory of holomorphic maps on taut manifolds, Italy: Mediterranean Press, 1989.
C. Carathéodory, Über eine spezielle Metrik, die in der Theorie der analytischen Funktionen auftritt, Atti Pontif. Accad. Sci. Nuovi Lincei 80 (1927), 135-141.
A. A. Fadlalla, On the group of automorphism of the Euclidean hypersphere, Mathematika 15 (1968), 193-198.
A. A. Fadlalla, On the boundary behaviour of the Carathéodory and Kobayashi distances in strongly pseudoconvex domains in $ℂ^{n}$ , Proc. Int. Workshop in Wuppertal (1990), Aspects of Mathematics (1990), 111-114.
A. A. Fadlalla, The Carathéodory distance in strongly pseudoconvex domains, Math. Ann. 298 (1994), 141-144.
F. Forestneric, J. P. Rosay, Localization of the Kobayashi metric and the boundary continuity of proper holomorphic mappings, Math. Ann. 279 (1987), 239-252.
E. Vesentini, Complex geodesic, Compositio Math. 44 (1981), 375-394.
N. Vormoor, Topologische Fortsetzung biholomorpher Funktionen auf den Rand bei beschränkten streng-pseudokonvexen Gebieten in $ℂ^{n}$ , Math. Ann. 204 (1973), 239-261.