Hyperbolic-like manifolds, geometrical properties and holomorphic mappings
Banach Center Publications (1996)
- Volume: 37, Issue: 1, page 53-66
- ISSN: 0137-6934
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topBoryczka, Grzegorz, and Tovar, Luis. "Hyperbolic-like manifolds, geometrical properties and holomorphic mappings." Banach Center Publications 37.1 (1996): 53-66. <http://eudml.org/doc/208616>.
@article{Boryczka1996,
abstract = {The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance $ρ_\{X\}^\{α\}(z_0,z)[]$ 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.},
author = {Boryczka, Grzegorz, Tovar, Luis},
journal = {Banach Center Publications},
keywords = {Dirichlet integral-type biholomorphic-invariant pseudo-distance; bordered holomorphic chains; hyperbolic-like manifolds; Stein manifolds},
language = {eng},
number = {1},
pages = {53-66},
title = {Hyperbolic-like manifolds, geometrical properties and holomorphic mappings},
url = {http://eudml.org/doc/208616},
volume = {37},
year = {1996},
}
TY - JOUR
AU - Boryczka, Grzegorz
AU - Tovar, Luis
TI - Hyperbolic-like manifolds, geometrical properties and holomorphic mappings
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 53
EP - 66
AB - The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance $ρ_{X}^{α}(z_0,z)[]$ 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.
LA - eng
KW - Dirichlet integral-type biholomorphic-invariant pseudo-distance; bordered holomorphic chains; hyperbolic-like manifolds; Stein manifolds
UR - http://eudml.org/doc/208616
ER -
References
top- [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. Zbl0358.32018
- [2] A. Andreotti and W. Stoll, Extension of holomorphic maps, Ann. of Math. (2) 72 (1960), 312-349. Zbl0095.28101
- [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. Zbl0202.11603
- [4] P. Dolbeault, Sur les chaines maximalement complexes au bord donné, Proc. Sympos. Pure Math. 44 (1986), 171-205.
- [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.
- [6] J. King, The currents defined by analytic varieties, Acta Math. 127 (1971), 185-220. Zbl0224.32008
- [7] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, Inc., New York 1970. Zbl0207.37902
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