Some counterexamples concerning intrinsic distances
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- by Theodore J. Barth PDF
- Proc. Amer. Math. Soc. 66 (1977), 49-53 Request permission
Abstract:
Examples of the following are given: (i) complex spaces whose Carathéodory distances are not inner; (ii) a taut complex space that is not complete hyperbolic; (iii) a complex space that is complete hyperbolic $\bmod \; \Delta$ but not taut $\bmod \; \Delta$; (iv) a bounded pseudoconvex domain that is not taut.References
- Theodore J. Barth, The Kobayashi distance induces the standard topology, Proc. Amer. Math. Soc. 35 (1972), 439–441. MR 306545, DOI 10.1090/S0002-9939-1972-0306545-X N. Kerzman, Taut manifolds and domains of holomorphy in ${{\mathbf {C}}^n}$, Notices Amer. Math. Soc. 16 (1969), 675-676. Abstract #69T-B120.
- Peter Kiernan, On the relations between taut, tight and hyperbolic manifolds, Bull. Amer. Math. Soc. 76 (1970), 49–51. MR 252678, DOI 10.1090/S0002-9904-1970-12363-1
- Shoshichi Kobayashi and Peter Kiernan, Holomorphic mappings into projective space with lacunary hyperplanes, Nagoya Math. J. 50 (1973), 199–216. MR 326007
- Shoshichi Kobayashi, Invariant distances on complex manifolds and holomorphic mappings, J. Math. Soc. Japan 19 (1967), 460–480. MR 232411, DOI 10.2969/jmsj/01940460
- Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
- Shoshichi Kobayashi, Some remarks and questions concerning the intrinsic distance, Tohoku Math. J. (2) 25 (1973), 481–486. MR 330519, DOI 10.2748/tmj/1178241281
- Shoshichi Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), no. 3, 357–416. MR 414940, DOI 10.1090/S0002-9904-1976-14018-9
- Hans-Jörg Reiffen, Die Carathéodorysche Distanz und ihre zugehörige Differentialmetrik, Math. Ann. 161 (1965), 315–324 (German). MR 196133, DOI 10.1007/BF01359970
- Frédéric Riesz, Sur les Fonctions Subharmoniques et Leur Rapport à la Théorie du Potentiel, Acta Math. 48 (1926), no. 3-4, 329–343 (French). MR 1555229, DOI 10.1007/BF02565338
- Nessim Sibony, Prolongement analytique des fonctions holomorphes bornées, C. R. Acad. Sci. Paris Sér. A-B 275 (1972), A973–A976 (French). MR 318515
- Nessim Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), no. 3, 205–230 (French). MR 385164, DOI 10.1007/BF01389850
- Hassler Whitney, Complex analytic varieties, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0387634
- H. Wu, Normal families of holomorphic mappings, Acta Math. 119 (1967), 193–233. MR 224869, DOI 10.1007/BF02392083
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 49-53
- MSC: Primary 32H15; Secondary 32H20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0454078-7
- MathSciNet review: 0454078