TY - JOUR
AU - Aytuna, A.
AU - Sadullaev, A.
PY - 2014/01/17
Y2 - 2024/05/29
TI - Parabolic Stein Manifolds
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 114
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-16640
UR - https://www.mscand.dk/article/view/16640
SP - 86-109
AB - 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.
ER -