scholarly journals Conformal Embeddings of an Open Riemann Surface into Another — A Counterpart of Univalent Function Theory —

2019 ◽  
Vol 25 (1) ◽  
pp. 23-31
Author(s):  
Masakazu SHIBA
Keyword(s):  
Riemann Surface ◽  
Univalent Function ◽  
Function Theory ◽  
Open Riemann Surface ◽  
Conformal Embeddings

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 An application of hypergeometric functions to a problem in function theory

1984 ◽  
Vol 7 (3) ◽  
pp. 503-506 ◽  
Author(s):  
Daniel S. Moak
Keyword(s):  
Recent Work ◽  
Univalent Function ◽  
Hypergeometric Functions ◽  
Function Theory ◽  
Alpha Beta

In some recent work in univalent function theory, Aharonov, Friedland, and Brannan studied the series(1+xt)α(1−t)β=∑n=0∞An(α,β)(x)tn. Brannan posed the problem of determiningS={(α,β):|An(α,β)(eiθ)|<|An(α,β)(1)|,   0<θ<2π,   α>0,   β>0,   n=1,2,3,…}. Brannan showed that ifβ≥α≥0, andα+β≥2, then(α,β)∈S. He also proved that(α,1)∈Sforα≥1. Brannan showed that for0<α<1andβ=1, there exists aθsuch that|A2k(α,1)e(iθ)|>|A2k(α,1)(1)|forkany integer. In this paper, we show that(α,β)∈Sforα≥1andβ≥1.

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 Applications of convolution operators to problems in univalent function theory.

1980 ◽  
Vol 27 (1) ◽  
pp. 81-94 ◽  
Author(s):  
Roger W. Barnard ◽  
Charles Kellogg
Keyword(s):  
Univalent Function ◽  
Function Theory ◽  
Convolution Operators
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