Parabolic Stein Manifolds

Details Parabolic Stein Manifolds Parabolic Stein Manifolds

2011-12-07

arxiv.org/abs/1112.1626v1

Mathematics

Complex Variables

Scientific paper

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 them. 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.

Affiliated with

Also associated with

No associations

Rating

Parabolic Stein Manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Parabolic Stein Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Parabolic Stein Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-598388