66 research outputs found
Geometric properties of semitube domains
In the paper we study the geometry of semitube domains in . In
particular, we extend the result of Burgu\'es and Dwilewicz for semitube
domains dropping out the smoothness assumption. We also prove various
properties of non-smooth pseudoconvex semitube domains obtaining among others a
relation between pseudoconvexity of a semitube domain and the number of
connected components of its vertical slices.
Finally, we present an example showing that there is a non-convex domain in
such that its image under arbitrary isometry is pseudoconvex.Comment: 6 page
Construction of labyrinths in pseudoconvex domains
We build in a given pseudoconvex (Runge) domain of a
convex set , every connected component of which is a
holomorphically contractible (convex) compact set, enjoying the property that
any continuous path with and omitting has infinite length. This
solves a problem left open in a recent paper by Alarc\'on and Forstneri\v{c}
Lower estimates of the Kobayashi distance and limits of complex geodesics
It is proved for a strongly pseudoconvex domain in with
-smooth boundary that any complex geodesic through every
two close points of sufficiently close to and whose difference
is non-tangential to intersect a compact subset of that
depends only on the rate of non-tangentiality. As an application, a lower bound
for the Kobayashi distance is obtained.Comment: v2: to appear in Math. An
Holomorphic maps acting as Kobayashi isometries on a family of geodesics
Consider a holomorphic map between two domains in . Let denote a family of geodesics for the Kobayashi
distance, such that acts as an isometry on each element of .
This paper is dedicated to characterizing the scenarios in which the
aforementioned condition implies that is a biholomorphism. Specifically, we
establish this when is a complete hyperbolic domain, and
comprises all geodesic segments originating from a specific point. Another case
is when and are -smooth bounded pseudoconvex domains, and
consists of all geodesic rays converging at a designated boundary
point of . Furthermore, we provide examples to demonstrate that these
assumptions are essentially optimal
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