Summary
Questions of non-uniqueness for the complex geodesics of a balanced convex domain D in a locally convex Hausdorff vector space E are investigated. The results establish a precise relationship between the shape of the boundary of D at a point y and the structure of the family of complex geodesics «near» ξ ↦ ξy. The case in which E is a Banach space is also considered and a complete description of all the complex geodesics is given for the open unit ball of the space C(X) of all the complex valued continuous functions on a compact Hausdorff space X.
Article PDF
Similar content being viewed by others
References
L. V. Ahlfors,Conformal Invariance. Topics in Geometric Functions Theory, McGraw-Hill, New York, 1973.
S.Dineen - R. M.Timoney - J.-P.Vigué,Pseudodistances Invariantes sur les Domains d'un Espace Localement Convexe, to appear.
T. Franzoni -E. Vesentini,Holomorphic Maps and Invariant Distances, North Holland, Amsterdam, 1980.
L. Lempert,La Métrique de Kobayashi et la Representation des Domaines sur la Boule, Bull. Soc. Math. France,109 (1981), pp. 427–474.
P. Noverraz,Pseudo-Convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie, North-Holland, Amsterdam, 1973.
H.Royden - P.-M.Wong,Carathéodory and Kobayashi Metric on Convex Domains, to appear.
E. Vesentini,Variations on a Theme of Carathéodory, Ann. Scuola Norm. Sup. Pisa,7 (1979), pp. 39–68.
E. Vesentini,Complex Geodesics, Compositio Mathematica,44 (1981), pp. 375–394.
E. Vesentini,Invariant Distances and Invariant Differential Metrics in Locally Convex Spaces, Proc. Stefan Banach International Mathematical Center,8 (1982), pp. 493–512.
E. Vesentini,Complex Geodesics and Holomorphic Maps, Symposia Mathematica,26 (1982), pp. 211–230.
J.-P. Vigué,Caractérisation des Automorphismes Analytiques d'un Domain Convexe Borné, C. R. Acad. Sci. Paris,299 (1984), pp. 101–105.
J.-P. Vigué,Geodesiques Complexes et Points Fixes d'Applications Holomorphes, Adv. in Math.,52 (1984), pp. 241–247.
J.-P.Vigué,Points Fixes d'Applications Holomorphes dans un Domain Borné Convexe de Cn, Trans. Amer. Math. Soc., to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gentili, G. On complex geodesics of balanced convex domains. Annali di Matematica pura ed applicata 144, 113–130 (1986). https://doi.org/10.1007/BF01760814
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01760814