Hyperbolic-like manifolds, geometrical properties and holomorphic mappings
Boryczka, Grzegorz ; Tovar, Luis
Banach Center Publications, Tome 37 (1996), p. 53-66 / Harvested from The Polish Digital Mathematics Library

The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance ρXα(z0,z)[] introduced by Dolbeault and Ławrynowicz (1989) in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:208616
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     title = {Hyperbolic-like manifolds, geometrical properties and holomorphic mappings},
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     volume = {37},
     year = {1996},
     pages = {53-66},
     zbl = {0887.46006},
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Boryczka, Grzegorz; Tovar, Luis. Hyperbolic-like manifolds, geometrical properties and holomorphic mappings. Banach Center Publications, Tome 37 (1996) pp. 53-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p53bwm/

[000] [1] A. Andreotti and J. Ławrynowicz, On the generalized complex Monge-Ampère equation on complex manifold and related questions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 943-948. | Zbl 0358.32018

[001] [2] A. Andreotti and W. Stoll, Extension of holomorphic maps, Ann. of Math. (2) 72 (1960), 312-349. | Zbl 0095.28101

[002] [3] S. S. Chern, H.I. Levine, and L. Nirenberg, Intrinsic norms on a complex manifold, Global Analysis, Papers in honor of K. Kodaira, ed. by D. C. Spencer and S. Iynaga, Univ. of Tokyo Press and Princeton Univ. Press, Tokyo 1969; reprinted in S. S. Chern: Selected papers, Springer Verlag, New York-Heidelberg-Berlin 1978, 371-391. | Zbl 0202.11603

[003] [4] P. Dolbeault, Sur les chaines maximalement complexes au bord donné, Proc. Sympos. Pure Math. 44 (1986), 171-205.

[004] [5] P. Dolbeault and J. Ławrynowicz, Holomorphic chains and extendability of holomorphic mappings, Deformations of Mathematical Structures. Complex Analysis with Physical Applications. Selected papers from the Seminar on Deformations, Łódź-Lublin 1985/87, ed. by J. Ławrynowicz, Kluwer Academic Publishers, Dordrecht-Boston-London 1989, 191-204.

[005] [6] J. King, The currents defined by analytic varieties, Acta Math. 127 (1971), 185-220. | Zbl 0224.32008

[006] [7] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, Inc., New York 1970. | Zbl 0207.37902