Warianty tytułu
Języki publikacji
Abstrakty
We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in $ℂ^n$ then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
143-148
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-05-09
poprawiono
1990-10-10
Twórcy
autor
- Department of Mathematics, Pedagogical Institute of Ha Noi N°I, Ha Noi, Viet Nam
Bibliografia
- [1] T. Barth, Taut and tight manifolds, Proc. Amer. Math. Soc. 24 (1970), 429-431.
- [2] T. Barth, Convex domains and Kobayashi hyperbolicity, ibid. 79 (1980), 556-558.
- [3] S. Dineen, R. Timoney et J.-P. Vigué, Pseudodistances invariantes sur les domaines d'un espace localement convexe, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 12 (1985), 515-529.
- [4] R. E. Edwards, Functional Analysis, Holt, Rinehart and Winston, New York 1965.
- [5] G. Fischer, Complex Analytic Geometry, Lecture Notes in Math. 538, Springer, 1976.
- [6] T. Franzoni and E. Vesentini, Holomorphic Maps and Invariant Distances, North-Holland Math. Stud. 40, Amsterdam 1980.
- [7] P. Kiernan, On the relations between taut, tight and hyperbolic manifolds, Bull. Amer. Math. Soc. 76 (1970), 49-51.
- [8] J. L. Kelley, General Topology, Van Nostrand, New York 1957.
- [9] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Dekker, New York 1970.
- [10] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474.
- [11] L. Lempert, Holomorphic retracts and intrinsic metrics in convex domains, Anal. Math. 8 (1982), 257-261.
- [12] H. L. Royden and P. Wong, Carathéodory and Kobayashi metrics on convex domains, to appear.
- [13] E. Vesentini, Complex geodesics, Compositio Math. 44 (1981), 375-394.
- [14] E. Vesentini, Complex geodesics and holomorphic maps, in: Sympos. Math. 26, Inst. Naz. Alta Mat. Fr. Severi, 1982, 211-230.
- [15] J.-P. Vigué, Points fixes d'applications holomorphes dans un domaine borné convexe de $ℂ^n$, Trans. Amer. Math. Soc. 289 (1985), 345-353.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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