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Hyperbolic-like manifolds, geometrical properties and holomorphic mappings. (English) Zbl 0887.46006

Ławrynowicz, J. (ed.), Generalizations of complex analysis and their applications in physics. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 37, 53-66 (1996).
Summary: The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudo-distance \(\rho^\alpha_X(z_0, z)[{\mathcal U}]\) introduced by P. Dolbeault and J. Ławrynowicz [Sel. Pap. Semin. Łodz/Poland 1985/87, 191-204 (1989; Zbl 0663.32018)] 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.
For the entire collection see [Zbl 0856.00020].

MSC:

46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.)
32H25 Picard-type theorems and generalizations for several complex variables
32G81 Applications of deformations of analytic structures to the sciences

Citations:

Zbl 0663.32018
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