Hyperbolic-like manifolds, geometrical properties and holomorphic mappings

• Autorzy: Grzegorz Boryczka , Luis Manuel Tovar
• Języki publikacji: EN

Abstrakty

EN

The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance $ρ_{X}^{α}(z_0,z)[𝓤]$ 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 53-66

Daty

wydano

1996

Twórcy

autor

Grzegorz Boryczka

• Institute of Mathematics, Polish Academy of Sciences, Narutowicza 56, PL-90-136 Łódź, Poland

autor

Luis Manuel Tovar

• Departamento de Matemáticas, E.S.F.M., Instituto Politécnico Nacional, U.P.A.L.M., Edifico No. 9, Zacatenco, 07000 México 14, D. F., México

Bibliografia

• [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.
• [2] A. Andreotti and W. Stoll, Extension of holomorphic maps, Ann. of Math. (2) 72 (1960), 312-349.
• [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.
• [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.
• [7] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, Inc., New York 1970.