Boundary Behavior of General Kobayashi Metrics on h-Extendible Domains
Main Article Content
Abstract
The purpose of this article is to prove the existence of -nontangential limits of the general Kobayashi metrics at -extendible boundary point. This is a generalization of Yu’s result for -nontangential limits.
Keywords:
General Kobayashi metrics; h-extendible models; Pseudoconvex domains; Finite type.
References
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R. Greene, S. Krantz, Stability of The Carathéodory and Kobayashi Metrics and Applications to Biholomorphic Mappings, in Complex Analysis of Several Complex Variables, Proc. Sympos. Pure Math., Vol. 41, 1984,
pp. 77-93, https://doi.org/10.1090/pspum/041/740874.
J. Yu, Weighted Boundary Limits of The Generalized Kobayashi-Royden Metrics on Weakly Pseudoconvex Domains, Trans. Amer. Math. Soc, Vol. 347, No. 2, 1995, pp. 587-614, https://www.jstor.org/stable/2154903 (accessed on: May 1st, 2024).
J. Yu, Peak Functions on Weakly Pseudoconvex Domains, Indiana Univ. Math. J, Vol. 43, No. 4, 1994,
pp. 1271-1295, https://www.jstor.org/stable/24898109 (accessed on: May 1st, 2024).
D. Catlin, Estimates of Invariant Metrics on Pseudoconvex Domains of Dimension Two, Math. Z Vol. 200, No. 3, 1989, pp. 429-466, https://doi.org/10.1007/bf01215657.
J. Chen, Estimates of the Invariant Metrics on Convex Domains, Purdue University Ph.D. Dissertation, 1989.
S. Cho, A Lower Bound on The Kobayashi Metric Near a Point of Finite Type in , J. Geo. Anal., Vol. 2, 1992, pp. 317-325, https://doi.org/10.1007/bf02934584.
K. Diederich, J. Fornæss, Proper Holomorphic Maps onto Pseudoconvex Domains with Real Analytic Boundary, Ann. of Math, Vol. 110, No. 3, 1979, pp. 575-592, https://doi.org/10.2307/1971240.
S. Frankel, Applications of Affine Geometry to Geometric Function Theory in Several Complex Variables, Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, Vol. 52, 1991, pp. 183-208, https://doi.org/10.1090/pspum/052.2/1128543.
G. Herbort, Invariant Metrics and Peak Functions on Pseudoconvex Domains of Homogeneous Finite Diagonal Type, Math. Z, Vol. 209, 1992, pp. 223-243, https://doi.org/10.1007/bf02570831.
S. Krantz, The Boundary Behavior of The Kobayashi Metric, Rocky Mountain J. Math, Vol. 22, No. 1, 1992,
pp. 227-234, https://doi.org/10.1216/rmjm/1181072807.
I. Graham, Boundary Behavior of The Carathéodory and Kobayashi Metrics on Strongly Pseudoconvex Domains in C^n with Smooth Boundary, Trans. Amer. Math. Soc, Vol. 207, 1975, pp. 219-240, https://doi.org/10.2307/1997175.
N. V. Thu, N. Q. Dieu, Some Properties of h-extendible Domains in C^(n+1), J. Math. Anal. Appl, Vol. 485, No. 2, 2020, 123810, 14 pp, https://doi.org/10.1016/j.jmaa.2019.123810.
R. Greene, S. Krantz, Stability of The Carathéodory and Kobayashi Metrics and Applications to Biholomorphic Mappings, in Complex Analysis of Several Complex Variables, Proc. Sympos. Pure Math., Vol. 41, 1984,
pp. 77-93, https://doi.org/10.1090/pspum/041/740874.