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1991 | 55 | 1 | 169-189
Tytuł artykułu

Invariant pseudodistances and pseudometrics - completeness and product property

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A survey of properties of invariant pseudodistances and pseudometrics is given with special stress put on completeness and product property.
Słowa kluczowe
Rocznik
Tom
55
Numer
1
Strony
169-189
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-08-17
Twórcy
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
autor
  • Fachbereich, Naturwissenschaften, Mathematik, Universität Osnabrück, Standort Vechta, Postfach 15 53, 2848 Vechta, Germany
Bibliografia
  • [1] K. Azukawa, Two intrinsic pseudo-metrics with pseudoconvex indicatrices and starlike circular domains, J. Math. Soc. Japan 38 (1986), 627-647.
  • [2] K. Azukawa, The invariant pseudometric related to negative pluri-subharmonic functions, Kodai Math. J. 10 (1987), 83-92.
  • [3] K. Azukawa, A note on Carathéodory and Kobayashi pseudodistances, preprint, 1990.
  • [4] T. J. Barth, The Kobayashi distance induces the standard topology, Proc. Amer. Math. Soc. 35 (1972), 439-441.
  • [5] T. J. Barth, Some counterexamples concerning intrinsic distances, ibid. 66 (1977), 49-53.
  • [6] T. J. Barth, The Kobayashi indicatrix at the center of a circular domain, ibid. 88 (1983), 527-530.
  • [7] E. Bedford and J. E. Fornæss, A construction of peak functions on weakly pseudoconvex domains, Ann. of Math. 107 (1978), 555-568.
  • [8] J. Burbea, The Carathéodory metric in plane domains, Kodai Math. Sem. Rep. 29 (1977), 157-166.
  • [9] J. Burbea, Inequalities between intrinsic metrics, Proc. Amer. Math. Soc. 67 (1977), 50-54.
  • [10] H. Busemann, Recent Synthetic Differential Geometry, Springer, Berlin 1970.
  • [11] D. Catlin, Boundary behavior of holomorphic functions on pseudoconvex domains, J. Differential Geom. 15 (1980), 605-625.
  • [12] D. Catlin, Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z. 200 (1989), 429-466.
  • [13] R. Courant und D. Hilbert, Methoden der mathematischen Physik I, Springer, Berlin 1968.
  • [14] J.-P. Demailly, Mesures de Monge-Ampère et mesures pluriharmoniques, Math. Z. 194 (1987), 519-564.
  • [15] S. Dineen, The Schwarz Lemma, Clarendon Press, Oxford 1989.
  • [16] A. Eastwood, A propos des variétés hyperboliques complètes, C. R. Acad. Sci. Paris 280 (1975), 1071-1075.
  • [17] A. A. Fadlalla, Quelques propriétés de la distance de Carathéodory, in: 7th. Arab. Sc. Congr., Cairo II (1973), 1-16.
  • [18] J. E. Fornæss and N. Sibony, Construction of p.s.h. functions on weakly pseudoconvex domains, Duke Math. J. 58 (1989), 633-655.
  • [19] T. Franzoni and E. Vesentini, Holomorphic Maps and Invariant Distances, North-Holland Math. Stud. 40, North-Holland, Amsterdam 1980.
  • [20] K. T. Hahn, On the completeness of the Bergman metric and its subordinate metrics, II, Pacific J. Math. 68 (1977), 437-446.
  • [21] M. Hakim et N. Sibony, Spectre de A(Ω̅) pour des domaines bornés faiblement pseudoconvexes réguliers, J. Funct. Anal. 37 (1980), 127-135.
  • [22] L. A. Harris, Schwarz-Pick systems of pseudometrics for domains in normed linear spaces, in: Advances in Holomorphy, J. A. Barroso (ed.), North-Holland Math. Stud. 34, North-Holland, Amsterdam 1979, 345-406.
  • [23] M. Jarnicki and P. Pflug, Effective formulas for the Carathéodory distance, Manusripta Math. 62 (1988), 1-20.
  • [24] M. Jarnicki and P. Pflug, The Carathéodory pseudodistance has the product property, Math. Ann. 285 (1989), 161-164.
  • [25] M. Jarnicki and P. Pflug, Bergman completeness of complete circular domains, Ann. Polon. Math. 50 (1989), 219-222.
  • [26] M. Jarnicki and P. Pflug, A counterexample for Kobayashi completeness of balanced domains, Proc. Amer. Math. Soc., to appear.
  • [27] M. Jarnicki and P. Pflug, The simplest example for the non-innerness of the Carathéodory distance, Results in Math. 18 (1990), 57-59.
  • [28] M. Jarnicki and P. Pflug, Some remarks on the product property for invariant pseudometrics, in: Proc. Sympos. Pure Math., to appear.
  • [29] M. Klimek, Extremal plurisubharmonic functions and invariant pseudodistances, Bull. Soc. Math. France 113 (1985), 123-142.
  • [30] M. Klimek, Infinitesimal pseudo-metrics and the Schwarz Lemma, Proc. Amer. Math. Soc. 105 (1989), 134-140.
  • [31] S. Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc. 82 (3) (1976), 357-416.
  • [32] A. Kodama, On boundedness of circular domains, Proc. Japan. Acad. 58 (1982), 227-230.
  • [33] S. G. Krantz, Function Theory of Several Complex Variables, Wiley-Interscience, New York 1982.
  • [34] S. Lang, Introduction to Complex Hyberbolic Spaces, Springer, Berlin 1987.
  • [35] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474.
  • [36] L. Lempert, Holomorphic retracts and intrinsic metrics in convex domains, Anal. Math. 8 (1982), 257-261.
  • [37] L. Lempert, Intrinsic distances and holomorphic retracts, in: Complex Analysis and Applications '81, Sofia 1984, 341-364.
  • [38] T. Mazur, P. Pflug and M. Skwarczyński, Invariant distances related to the Bergman function, Proc. Amer. Math. Soc. 94 (1985), 72-76.
  • [39] T. Ohsawa, A remark on the completeness of the Bergman metric, Proc. Japan Acad. 57 (1981), 238-240.
  • [40] P. Pflug, About the Carathéodory completeness of all Reinhardt domains, in: Functional Analysis, Holomorphy and Approximation Theory II, North-Holland, 1984, 331-337.
  • [41] E. A. Poletskiĭ and B. V. Shabat, Invariant metrics, in: Encyclopaedia of Mathematical Sciences, Vol. 9, Springer, 1989, 63-111.
  • [42] H. J. Reiffen, Die Carathéodorysche Distanz und ihr zugehörige Differentialmetrik, Math. Ann. 161 (1965), 315-324.
  • [43] W. Rinow, Die innere Geometrie der metrischen Räume, Grundlehren Math. Wiss. 105, Springer, Berlin 1961.
  • [44] R. M. Robinson, Analytic functions on circular rings, Duke Math. J. 10 (1943), 341-354.
  • [45] H. L. Royden, Remarks on the Kobayashi metric, in: Lecture Notes in Math. 185 Springer, 1971, 125-137.
  • [46] N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230.
  • [47] N. Sibony, A class of hyperbolic manifolds, in: Ann. of Math. Stud. 100, Princeton Univ. Press, Princeton, N.J., 1981, 357-372.
  • [48] J. Siciak, Balanced domains of holomorphy of type $H^∞$, Mat. Vesnik 37 (1985), 134-144.
  • [49] R. R. Simha, The Carathéodory metric on the annulus, Proc. Amer. Math. Soc. 50 (1975), 162-166.
  • [50] M. Suzuki, The generalized Schwarz Lemma for the Bergman metric, Pacific J. Math. 117 (1985), 429-442.
  • [51] S. Venturini, Comparison between the Kobayashi and Carathéodory distances on strongly pseudoconvex bounded domains in $ℂ^n$, Proc. Amer. Math. Soc. 107 (1989), 725-730.
  • [52] E. Vesentini, Complex geodesics and holomorphic maps, Sympos. Math. 26 (1982), 211-230.
  • [53] J.-P. Vigué, La distance de Carathéodory n'est pas intérieure, Resultate Math. 6 (1983), 100-104.
  • [54] J.-P. Vigué, The Carathéodory distance does not define the topology, Proc. Amer. Math. Soc. 91 (1984), 223-224.
  • [55] M. Jarnicki, P. Pflug and J.-P. Vigué, The Carathéodory distance does not define the topology - the case of domains, C. R. Acad. Sci. Paris 312 (1991), 77-79.
  • [56] M. Jarnicki and P. Pflug, The inner Carathéodory distance for the annulus, Math. Ann. 289 (1991), 335-339.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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