Parabolic stein manifolds
Aytuna, Aydın and Sadullaev, Azimbay (2011) Parabolic stein manifolds. [Working Paper / Technical Report] Sabanci University ID:arXiv:1112.1626v1 [math.CV] 7 Dec 2011
An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for Stein manifolds of arbitrary dimension. In the first part of this note we compile these notions of parabolicity and give some immediate relations among these different definitions. In section 3 we relate some of these notions to the linear topological type of the Fr´echet space of analytic functions on the given manifold. In sections 4 and 5 we look at some examples and show, for example, that the complement of the zero set of a Weierstrass polynomial possesses a continuous plurisubharmonic exhaustion function that is maximal off a compact subset.
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