scholarly journals Simultaneous approximation on two subsets of an open Riemann surface

2006 ◽  
Vol 138 (2) ◽  
pp. 151-167
Author(s):  
André Boivin ◽  
Paul M. Gauthier ◽  
Gerald Schmieder
Keyword(s):  
Riemann Surface ◽  
Simultaneous Approximation ◽  
Open Riemann Surface

scholarly journals Analytic Functions on Some Riemann Surfaces

1963 ◽  
Vol 22 ◽  
pp. 211-217 ◽  
Author(s):  
Nobushige Toda ◽  
Kikuji Matsumoto
Keyword(s):  
Riemann Surface ◽  
Compact Subset ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Open Riemann Surface ◽  
Interesting Theorem ◽  
Hyperbolic Riemann Surface

Some years ago, Kuramochi gave in his paper [5] a very interesting theorem, which can be stated as follows.THEOREM OF KURAMOCHI. Let R be a hyperbolic Riemann surface of the class Of OHR(OHD,resp.). Then, for any compact subset K of R such that R—K is connected, R—K as an open Riemann surface belongs to the class 0AB(OAD resp.).

scholarly journals Boundary Isomorphism between Dirichlet Finite Solutions of Δu = Pu and Harmonic Functions

1973 ◽  
Vol 50 ◽  
pp. 7-20 ◽  
Author(s):  
Ivan J. Singer
Keyword(s):  
Differential Equation ◽  
Riemann Surface ◽  
Laplace Operator ◽  
Nontrivial Solution ◽  
Harmonic Functions ◽  
Green’S Functions ◽  
Hölder Continuous ◽  
Open Riemann Surface ◽  
Continuous Density ◽  
The Laplace Operator

Consider an open Riemann surface R and a density P(z)dxdy (z = x + iy), well defined on R. As was shown by Myrberg in [3], if P ≢ 0 is a nonnegative α-Hölder continuous density on R (0 < α ≤ 1) then there exists the Green’s functions of the differential equationp>on R, where Δ means the Laplace operator. As a consequence, there always exists a nontrivial solution on R.

scholarly journals P-harmonic dimensions on ends

1993 ◽  
Vol 132 ◽  
pp. 131-139
Author(s):  
Michihiko Kawamura ◽  
Shigeo Segawa
Keyword(s):  
Riemann Surface ◽  
Boundary Component ◽  
Harmonic Functions ◽  
Ideal Boundary ◽  
Boundary Values ◽  
Hölder Continuous ◽  
Closed Curves ◽  
Open Riemann Surface ◽  
Relative Boundary ◽  
Bounded Harmonic Functions

Consider an end Ω in the sense of Heins (cf. Heins [3]): Ω is a relatively non-compact subregion of an open Riemann surface such that the relative boundary ∂Ω consists of finitely many analytic Jordan closed curves, there exist no non-constant bounded harmonic functions with vanishing boundary values on ∂Ω and Ω has a single ideal boundary component. A density P = P(z)dxdy (z = x + iy) is a 2-form on Ω∩∂Ω with nonnegative locally Holder continuous coefficient P(z).

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 Open Riemann Surface with Null Boundary

1951 ◽  
Vol 3 ◽  
pp. 73-79 ◽  
Author(s):  
Kiyoshi Noshiro
Keyword(s):  
Riemann Surface ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Open Riemann Surface ◽  
Capacity Zero

Recently the writer has obtained some results concerning meromorphic or algebroidal functions with the set of essential singularities of capacity zero, with an aid of a theorem of Evans. In the present paper, suggested from recent interesting papers of Sario and Pfluger, the writer will extend his results to single-valued analytic functions defined on open abstract Riemann surfaces with null boundary in the sense of Nevanlinna, using a lemma instead of Evans’ theorem.

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