Topologies defined by some invariant pseudodistances
Barth, Theodore
Banach Center Publications, Tome 31 (1995), p. 69-76 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262804 
@article{bwmeta1.element.bwnjournal-article-bcpv31z1p69bwm,
     author = {Barth, Theodore},
     title = {Topologies defined by some invariant pseudodistances},
     journal = {Banach Center Publications},
     volume = {31},
     year = {1995},
     pages = {69-76},
     zbl = {0842.32018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p69bwm}
}

Barth, Theodore. Topologies defined by some invariant pseudodistances. Banach Center Publications, Tome 31 (1995) pp. 69-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p69bwm/

[000] [AnS] A. Andreotti and W. Stoll, Extension of holomorphic maps, Ann. of Math. (2) 72 (1960), 312-349 | Zbl 0095.28101

[001] [Au] V. Aurich, Bounded analytic sets in Banach spaces, Ann. Inst. Fourier (Grenoble) 36 (1986), 229-243 | Zbl 0591.46005

[002] [B72] T. J. Barth, The Kobayashi distance induces the standard topology, Proc. Amer. Math. Soc. 35 (1972), 439-441 | Zbl 0259.32007

[003] [B77] T. J. Barth, Some counterexamples concerning intrinsic distances, Proc. Amer. Math. Soc. 66 (1977), 49-53 | Zbl 0331.32019

[004] [C] C. Carathéodory, Über das Schwarzsche Lemma bei analytischen Funktionen von zwei komplexen Veränderlichen, Math. Ann. 97 (1926), 76-98 | Zbl 52.0345.02

[005] [Di] S. Dineen, The Schwarz Lemma Oxford University Press, 1989.

[006] [DiT] S. Dineen and R. M. Timoney, Complex geodesics on convex domains, in: Progress in Functional Analysis, North-Holland 1992, 333-365 | Zbl 0785.46044

[007] [DiTV] S. Dineen, R. M. Timoney et J.-P. Vigué, Pseudodistances invariantes sur les domaines d'un espace localement convexe, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 12 (1985), 515-529 | Zbl 0603.46052

[008] [Do] A. Douady, A remark on Banach analytic spaces, in: Symposium on Infinite Dimensional Topology, Princeton University Press 1972, 41-42

[009] [EaH] C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings in: Global Analysis (Berkeley, Calif. 1968), Proc. Sympos. Pure Math. 16,, Amer. Math. Soc. 1970, 61-65

[010] [ElG] Y. Eliashberg and M. Gromov, Embeddings of Stein manifolds of dimension n into the affine space of dimension 3n/2+1, Ann. of Math. (2) 136 (1992), 123-135 | Zbl 0758.32012

[011] [FS77] J. E. Fornaess and E. L. Stout, Spreading polydiscs on complex manifolds, Amer. J. Math. 99 (1977), 933-960 | Zbl 0384.32004

[012] [FS82] J. E. Fornaess and E. L. Stout, J. E. Fornaess, E. L. Stout, Regular holomorphic images of balls, Ann. Inst. Fourier (Grenoble) 32 (1982), 23-36 | Zbl 0452.32008

[013] [FV] T. Franzoni and E. Vesentini, Holomorphic Maps and Invariant Distances, North-Holland 1980. | Zbl 0447.46040

[014] [G] R. C. Gunning, On Vitali's theorem for complex spaces with singularities, J. Math. Mech. 8 (1959), 133-141 | Zbl 0092.07503

[015] [GR] R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall 1965. | Zbl 0141.08601

[016] [Ha] M. Hayashi, The maximal ideal space of the bounded analytic functions on a Riemann surface, J. Math. Soc. Japan 39 (1987), 337-344 | Zbl 0598.30070

[017] [He] M. Hervé, Analyticity in Infinite Dimensional Spaces, Walter de Gruyter 1989. | Zbl 0666.58008

[018] [Hi] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. (2) 79 (1964), 109-326 | Zbl 0122.38603

[019] [HiR] H. Hironaka and H. Rossi, On the equivalence of imbeddings of exceptional complex spaces, Math. Ann. 156 (1964), 313-333 | Zbl 0136.20801

[020] [JP90] M. Jarnicki and P. Pflug, The simplest example for the non-innerness of the Carathéodory distance, Results Math. 18 (1990), 57-59 | Zbl 0709.32015

[021] [JP91] M. Jarnicki and P. Pflug, M. Jarnicki, P. Pflug, Invariant pseudodistances and pseudometrics-completeness and the product property, Ann. Polon. Math. 55 (1991), 169-189 | Zbl 0756.32016

[022] [JPV91] 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 Sér. I Math. 312 (1991), 77-79 | Zbl 0721.32010

[023] [JPV92] M. Jarnicki, M. Jarnicki, P. Pflug, J.-P. Vigué, A remark on Carathéodory balls, Arch. Math. (Basel) 58 (1992), 595-598

[024] [K67] S. Kobayashi, Invariant distances on complex manifolds and holomorphic mappings, J. Math. Soc. Japan 19 (1967), 460-480 | Zbl 0158.33201

[025] [K70] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker 1970.

[026] [K73] S. Kobayashi, Some remarks and questions concerning the intrinsic distance, Tôhoku Math. J. (2) 25 (1973), 481-486 | Zbl 0281.32017

[027] [K76] S. Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), 357-416 | Zbl 0346.32031

[028] [K90] S. Kobayashi, A new invariant infinitesimal metric, Internat. J. Math. 1 (1990), 83-90 | Zbl 0702.32021

[029] [La] S. Lang, Introduction to Complex Hyperbolic Spaces, Springer 1987. | Zbl 0628.32001

[030] [Le] J. Lewittes, A note on parts and hyperbolic geometry, Proc. Amer. Math. Soc. 17 (1966), 1087-1090 | Zbl 0196.13801

[031] [Lo] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser 1991.

[032] [M] K. Menger, Untersuchungen über allgemeine Metrik. IV. Zur Metrik der Kurven, Math. Ann. 103 (1930), 466-501 | Zbl 56.0508.04

[033] [PS] E. A. Poletskiĭ and B. V. Shabat, Invariant metrics in: Complex Analysis-Several Variables 3, VINITI, Moscow, 1986 (in Russian); English transl.: Several Complex Variables III, Encyclopaedia Math. Sci. 9, Springer, 1989, 63-111

[034] [Re] H.-J. Reiffen, Die Carathéodorysche Distanz und ihre zugehörige Differentialmetrik, Math. Ann. 161 (1965), 315-324 | Zbl 0141.08803

[035] [Ri] W. Rinow, Die innere Geometrie der metrischen Räume, Springer 1961. | Zbl 0096.16302

[036] [Ro] H. L. Royden, Remarks on the Kobayashi metric in: Several Complex Variables II Maryland 1970, Lecture Notes in Math. 185,, Springer 1971, 125-137.

[037] [Sib] N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230 | Zbl 0333.32011

[038] [Siu] Y. T. Siu, Every Stein subvariety admits a Stein neighborhood ibid. 38 (1976), 89-100 | Zbl 0343.32014

[039] [Ve] S. Venturini, Pseudodistances and pseudometrics on real and complex manifolds, Ann. Mat. Pura Appl. (4) 154 (1989), 385-402 | Zbl 0702.32022

[040] [Vi83] J.-P. Vigué, La distance de Carathéodory n'est pas intérieure, Results Math. 6 (1983), 100-104 | Zbl 0552.32022

[041] [Vi84] J.-P. Vigué, The Carathéodory distance does not define the topology, Proc. Amer. Math. Soc. 91 (1984), 223-224 | Zbl 0555.32016

[042] [W] H. Wu, Normal families of holomorphic mappings, Acta Math. 119 (1967), 193-233 | Zbl 0158.33301