In mathematics, especially several complex variables, an open subset
The reason for studying these kinds of domains is that logarithmically convex Reinhardt domain are the domains of convergence of power series in several complex variables. Note that in one complex variable, a logarithmically convex Reinhardt domain is simply a disc.
The intersection of logarithmically convex Reinhardt domains is still a logarithmically convex Reinhardt domain, so for every Reinhardt domain, there is a smallest logarithmically convex Reinhardt domain which contains it.
A simple example of logarithmically convex Reinhardt domains is a polydisc, that is, a product of disks.
Thullen's classical result says that a 2-dimensional bounded Reinhard domain containing the origin is biholomorphic to one of the following domains provided that the orbit of the origin by the automorphism group has positive dimension:
(1)
(2)
(3)
In 1978, Toshikazu Sunada established a generalization of Thullen's result, and proved that two