TL;DR
This paper characterizes the automorphism group of the tetrablock, a complex domain with tetrahedral shape, and establishes a Schwarz lemma for it, revealing its geometric and symmetry properties.
Contribution
It determines the automorphism group of the tetrablock and describes its action via a natural foliation by complex geodesic discs.
Findings
The tetrablock is inhomogeneous.
The automorphism group is explicitly determined.
A Schwarz lemma for the tetrablock is proved.
Abstract
The tetrablock is a domain in 3-dimensional complex space that meets 3-dimensional Euclidean space in a regular tetrahedron. It is shown to be inhomogeneous and its automorphism group is determined. A type of Schwarz lemma for the tetrablock is proved. The action of the automorphism group is described in terms of a certain natural foliation of the tetrablock by complex geodesic discs.
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