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Article

Keywords:
Carathéodory metric; Kobayashi metric; Azukawa metric; convexifiable point
Summary:
The behaviour of the Carathéodory, Kobayashi and Azukawa metrics near convex boundary points of domains in $\mathbb{C}^n$ is studied.
References:
[1] K. Azukawa: The invariant pseudo-metric related to negative plurisubharmonic functions. Kodai Math.  J. 10 (1987), 83–92. DOI 10.2996/kmj/1138037363 | MR 0879385 | Zbl 0618.32020
[2] D. Coman: Boundary behavior of the pluricomplex Green function. Ark. Mat. 36 (1998), 341–353. DOI 10.1007/BF02384773 | MR 1650450 | Zbl 1021.32015
[3] H.  Gaussier: Tautness and complete hyperbolicity of domains in $\mathbb{C}^n$. Proc. Amer. Math. Soc. 127 (1999), 105–116. DOI 10.1090/S0002-9939-99-04492-5 | MR 1458872
[4] I.  Graham: Boundary behavior of the Carathédory and Kobayashi metrics on strongly pseudoconvex domains in $\mathbb{C}^n$ with smooth boundary. Trans. Amer. Math. Soc. 207 (1975), 219–240. MR 0372252
[5] M.  Klimek: Extremal plurisubharmonic function and invariant pseudodistances. Bull. Soc. Math. France 113 (1985), 231–240. MR 0820321
[6] J.  Kohn: Global regularity for $\bar{\partial }\Re $ on weakly pseudoconvex manifolds. Trans. Amer. Math. Soc. 181 (1973), 273–292. MR 0344703
[7] L.  Lempert: Holomorphic retracts and intrinsic metrics in convex domains. Analysis Mathematica 8 (1982), 257–261. DOI 10.1007/BF02201775 | MR 0690838 | Zbl 0509.32015
[8] N.  Nikolov: Localization, stability and boundary behavior of the Kobayashi metrics. Preprint ESI 790, Vienna, 1999, pp. 11. MR 1910713
[9] N.  Sibony: Une classe de domaines pseudoconvexes. Duke Math.  J. 55 (1987), 299–319. DOI 10.1215/S0012-7094-87-05516-5 | MR 0894582 | Zbl 0622.32016
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