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Barth, Theodore J.

The Kobayashi indicatrix at the center of a circular domain. (English) Zbl 0494.32008

Proc. Am. Math. Soc. 88, 527-530 (1983).
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Cited in 4 Reviews
Cited in 15 Documents

MSC:

32F45 Invariant metrics and pseudodistances in several complex variables
32T99 Pseudoconvex domains
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32E05 Holomorphically convex complex spaces, reduction theory
32K05 Banach analytic manifolds and spaces

Keywords:

Kobayashi metric; complete circular domain; taut domain; complex Banach space; convex domain; semigauge

Citations:

Zbl 0158.333; Zbl 0346.32031
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\textit{T. J. Barth}, Proc. Am. Math. Soc. 88, 527--530 (1983; Zbl 0494.32008)
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References:

[1] Theodore J. Barth, Taut and tight complex manifolds, Proc. Amer. Math. Soc. 24 (1970), 429 – 431. · Zbl 0191.09403
[2] C. Carathéodory, Über die Geometrie der analytischen Abbildungen, die durch analytische Funktionen von zwei Veränderlichen vermittelt werden, Abh. Math. Sem. Univ. Hamburg 6 (1928), 96-145. · JFM 54.0372.04
[3] Tullio Franzoni and Edoardo Vesentini, Holomorphic maps and invariant distances, Notas de Matemática [Mathematical Notes], vol. 69, North-Holland Publishing Co., Amsterdam-New York, 1980. · Zbl 0447.46040
[4] Lawrence A. Harris, Schwarz-Pick systems of pseudometrics for domains in normed linear spaces, Advances in holomorphy (Proc. Sem. Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977) North-Holland Math. Stud., vol. 34, North-Holland, Amsterdam-New York, 1979, pp. 345 – 406.
[5] Fritz Hartogs, Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen, insbesondere über die Darstellung derselben durch Reihen, welche nach Potenzen einer Veränderlichen fortschreiten, Math. Ann. 62 (1906), no. 1, 1 – 88 (German). · JFM 37.0444.01
[6] Norberto Kerzman and Jean-Pierre Rosay, Fonctions plurisousharmoniques d’exhaustion bornées et domaines taut, Math. Ann. 257 (1981), no. 2, 171 – 184 (French). · Zbl 0451.32012
[7] Shoshichi Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), no. 3, 357 – 416. · Zbl 0346.32031
[8] P. Noverraz, Pseudo-convexité, convexité polynomiale et domaines d’holomorphie en dimension infinie, North-Holland Math. Studies, 3, Notas Mat., 48, North-Holland, Amsterdam, 1973. · Zbl 0251.46049
[9] Peter Pflug, About the Carathéodory completeness of all Reinhardt domains, Functional analysis, holomorphy and approximation theory, II (Rio de Janeiro, 1981) North-Holland Math. Stud., vol. 86, North-Holland, Amsterdam, 1984, pp. 331 – 337. · Zbl 0536.32001
[10] H. Wu, Normal families of holomorphic mappings, Acta Math. 119 (1967), 193 – 233. · Zbl 0158.33301
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