On the domains where a harmonic or subharmonic function is positive

1976 ◽  
pp. 24-55
Author(s):  
W. K. Hayman
Keyword(s):  
Subharmonic Function

The Growth of the Hyperplane Mean of a Subharmonic Function

1987 ◽  
Vol s2-36 (3) ◽  
pp. 501-512 ◽  
Author(s):  
D. H. Armitage ◽  
S. J. Gardiner
Keyword(s):  
Subharmonic Function

The logarithm of the modulus of a holomorphic function as a minorant for a subharmonic function. II. The complex plane

2017 ◽  
Vol 101 (3-4) ◽  
pp. 590-607 ◽  
Author(s):  
T. Yu. Baiguskarov ◽  
B. N. Khabibullin ◽  
A. V. Khasanova
Keyword(s):  
Holomorphic Function ◽  
Complex Plane ◽  
Subharmonic Function

scholarly journals Parabolic Stein Manifolds

2014 ◽  
Vol 114 (1) ◽  
pp. 86 ◽  
Author(s):  
A. Aytuna ◽  
A. Sadullaev
Keyword(s):  
Riemann Surface ◽  
Subharmonic Function ◽  
Arbitrary Dimension ◽  
Topological Type ◽  
Zero Set ◽  
Space Of Analytic Functions ◽  
Exhaustion Function ◽  
Stein Manifolds ◽  
Open Riemann Surface ◽  
The Given

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.

scholarly journals On Level Curves of Harmonic and Analytic Functions on Riemann Surfaces

1969 ◽  
Vol 34 ◽  
pp. 77-87
Author(s):  
Shinji Yamashitad
Keyword(s):  
Riemann Surface ◽  
Subharmonic Function ◽  
Analytic Functions ◽  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Vector Lattice ◽  
Level Curves ◽  
Harmonic Majorant ◽  
Harmonic And Analytic Functions ◽  
Hyperbolic Riemann Surface

In this note we shall denote by R a hyperbolic Riemann surface. Let HP′(R) be the totality of harmonic functions u on R such that every subharmonic function | u | has a harmonic majorant on R. The class HP′(R) forms a vector lattice under the lattice operations:

scholarly journals RETRACTED ARTICLE: A new application of boundary integral behaviors of harmonic functions to the least harmonic majorant

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Minghua Han ◽  
Jianguo Sun ◽  
Gaoying Xue
Keyword(s):  
Subharmonic Function ◽  
Harmonic Functions ◽  
Boundary Integral ◽  
Retracted Article ◽  
New Type ◽  
Harmonic Majorant

Abstract Our main aim in this paper is to obtain a new type of boundary integral behaviors of harmonic functions in a smooth cone. As an application, the least harmonic majorant of a nonnegative subharmonic function is also given.

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