Invariant pseudodistances and pseudometrics - completeness and product property
Annales Polonici Mathematici (1991)
- Volume: 55, Issue: 1, page 169-189
- ISSN: 0066-2216
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topMarek Jarnicki, and Peter Pflug. "Invariant pseudodistances and pseudometrics - completeness and product property." Annales Polonici Mathematici 55.1 (1991): 169-189. <http://eudml.org/doc/262259>.
@article{MarekJarnicki1991,
abstract = {A survey of properties of invariant pseudodistances and pseudometrics is given with special stress put on completeness and product property.},
author = {Marek Jarnicki, Peter Pflug},
journal = {Annales Polonici Mathematici},
keywords = {survey; intrinsic pseudodistances; pseudometrics; Kobayashi; Carathéodory; product domains},
language = {eng},
number = {1},
pages = {169-189},
title = {Invariant pseudodistances and pseudometrics - completeness and product property},
url = {http://eudml.org/doc/262259},
volume = {55},
year = {1991},
}
TY - JOUR
AU - Marek Jarnicki
AU - Peter Pflug
TI - Invariant pseudodistances and pseudometrics - completeness and product property
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 169
EP - 189
AB - A survey of properties of invariant pseudodistances and pseudometrics is given with special stress put on completeness and product property.
LA - eng
KW - survey; intrinsic pseudodistances; pseudometrics; Kobayashi; Carathéodory; product domains
UR - http://eudml.org/doc/262259
ER -
References
top- [1] K. Azukawa, Two intrinsic pseudo-metrics with pseudoconvex indicatrices and starlike circular domains, J. Math. Soc. Japan 38 (1986), 627-647. Zbl0607.32015
- [2] K. Azukawa, The invariant pseudometric related to negative pluri-subharmonic functions, Kodai Math. J. 10 (1987), 83-92. Zbl0618.32020
- [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. Zbl0259.32007
- [5] T. J. Barth, Some counterexamples concerning intrinsic distances, ibid. 66 (1977), 49-53. Zbl0331.32019
- [6] T. J. Barth, The Kobayashi indicatrix at the center of a circular domain, ibid. 88 (1983), 527-530. Zbl0494.32008
- [7] E. Bedford and J. E. Fornæss, A construction of peak functions on weakly pseudoconvex domains, Ann. of Math. 107 (1978), 555-568. Zbl0392.32004
- [8] J. Burbea, The Carathéodory metric in plane domains, Kodai Math. Sem. Rep. 29 (1977), 157-166. Zbl0419.30010
- [9] J. Burbea, Inequalities between intrinsic metrics, Proc. Amer. Math. Soc. 67 (1977), 50-54. Zbl0346.32030
- [10] H. Busemann, Recent Synthetic Differential Geometry, Springer, Berlin 1970. Zbl0194.53701
- [11] D. Catlin, Boundary behavior of holomorphic functions on pseudoconvex domains, J. Differential Geom. 15 (1980), 605-625. Zbl0484.32005
- [12] D. Catlin, Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z. 200 (1989), 429-466. Zbl0661.32030
- [13] R. Courant und D. Hilbert, Methoden der mathematischen Physik I, Springer, Berlin 1968. Zbl0156.23201
- [14] J.-P. Demailly, Mesures de Monge-Ampère et mesures pluriharmoniques, Math. Z. 194 (1987), 519-564. Zbl0595.32006
- [15] S. Dineen, The Schwarz Lemma, Clarendon Press, Oxford 1989. Zbl0708.46046
- [16] A. Eastwood, A propos des variétés hyperboliques complètes, C. R. Acad. Sci. Paris 280 (1975), 1071-1075. Zbl0301.32021
- [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. Zbl0679.32017
- [19] T. Franzoni and E. Vesentini, Holomorphic Maps and Invariant Distances, North-Holland Math. Stud. 40, North-Holland, Amsterdam 1980. Zbl0447.46040
- [20] K. T. Hahn, On the completeness of the Bergman metric and its subordinate metrics, II, Pacific J. Math. 68 (1977), 437-446. Zbl0356.32017
- [21] M. Hakim et N. Sibony, Spectre de A(Ω̅) pour des domaines bornés faiblement pseudoconvexes réguliers, J. Funct. Anal. 37 (1980), 127-135. Zbl0441.46044
- [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. Zbl0656.32016
- [24] M. Jarnicki and P. Pflug, The Carathéodory pseudodistance has the product property, Math. Ann. 285 (1989), 161-164. Zbl0662.32023
- [25] M. Jarnicki and P. Pflug, Bergman completeness of complete circular domains, Ann. Polon. Math. 50 (1989), 219-222. Zbl0701.32002
- [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. Zbl0709.32015
- [28] M. Jarnicki and P. Pflug, Some remarks on the product property for invariant pseudometrics, in: Proc. Sympos. Pure Math., to appear. Zbl0747.32018
- [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. Zbl0346.32031
- [32] A. Kodama, On boundedness of circular domains, Proc. Japan. Acad. 58 (1982), 227-230. Zbl0515.32011
- [33] S. G. Krantz, Function Theory of Several Complex Variables, Wiley-Interscience, New York 1982. Zbl0471.32008
- [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. Zbl0509.32015
- [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. Zbl0534.32010
- [39] T. Ohsawa, A remark on the completeness of the Bergman metric, Proc. Japan Acad. 57 (1981), 238-240. Zbl0508.32008
- [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. Zbl0141.08803
- [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. Zbl0060.21804
- [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. Zbl0333.32011
- [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 , Mat. Vesnik 37 (1985), 134-144. Zbl0575.32009
- [49] R. R. Simha, The Carathéodory metric on the annulus, Proc. Amer. Math. Soc. 50 (1975), 162-166. Zbl0281.30010
- [50] M. Suzuki, The generalized Schwarz Lemma for the Bergman metric, Pacific J. Math. 117 (1985), 429-442. Zbl0573.32025
- [51] S. Venturini, Comparison between the Kobayashi and Carathéodory distances on strongly pseudoconvex bounded domains in , Proc. Amer. Math. Soc. 107 (1989), 725-730. Zbl0692.32013
- [52] E. Vesentini, Complex geodesics and holomorphic maps, Sympos. Math. 26 (1982), 211-230. Zbl0506.32008
- [53] J.-P. Vigué, La distance de Carathéodory n'est pas intérieure, Resultate Math. 6 (1983), 100-104. Zbl0552.32022
- [54] J.-P. Vigué, The Carathéodory distance does not define the topology, Proc. Amer. Math. Soc. 91 (1984), 223-224. Zbl0555.32016
- [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. Zbl0721.32010
- [56] M. Jarnicki and P. Pflug, The inner Carathéodory distance for the annulus, Math. Ann. 289 (1991), 335-339. Zbl0719.30036
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