Parabolic Stein manifolds

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Abstract

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 Fréchet space of analytic functions on the given manifold. In section 4 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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• Parabolic Stein manifolds. (deposited 17 May 2013 14:59)
  • Parabolic Stein manifolds. (deposited 18 Jun 2014 10:32) [Currently Displayed]