arXiv subjects
Publications and source records attributed to Arkadiusz Lewandowski.
We prove that given a family of strictly pseudoconvex domains varying in C2 topology on domains, there exists a continuously varying family of exposing maps for all boundary points of all domains.
We give the parameter version of localization theorem for Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of Graham-Kerzman is proved in the hereby paper, as well.
We give a parameter version of Graham-Kerzman approximation theorem for bounded holomorphic functions on strictly pseudoconvex domains. As an application, we present some uniform estimates for the boundary behaviour of the Kobayashi and Carathéodory pseudodistences on such domains.
We prove that given a family $(G_t)$ of strictly pseudoconvex domains varying in $\mathcal{C}^2$ topology on domains, there exists a continuously varying family of peak functions $h_{t,ζ}$ for all $G_t$ at every $ζ\in\partial G_t.$
The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of sets are given. In particular, continuity properties of Kobayashi and Carathéodory pseudodistances, as well as Lempert and Green functions with respect to sequences of domains converging in Hausdorff metric are delivered.
We discuss the problem of the existence of envelopes of holomorphy of the A-crosses, which leads us to the far-reaching generalizations of the famous Hartogs theorem. We also take under consideration the issue of the existence of "nice" general descriptions of envelopes of holomorphy of the cross-like objects in terms of the relative extremal function, which seems to be very natural in the light of the extension theory of separately holomorphic functions on classical crosses and (N,k)-crosses.
The main result of this paper is some "annulus" formula for the relative extremal function in the context of Stein spaces (Theorem 1.1). Our result may be useful in the theory of the extension of separately holomorphic functions on generalized (N,k)-crosses lying in the product of Stein manifolds (Theorem 4.6).