APPLICATION OF GENERALIZED ANALYTIC FUNCTIONS ON RIEMANN SURFACES TO THE INVESTIGATION OF $ G$-DEFORMATIONS OF TWO-DIMENSIONAL SURFACES IN $ E^4$

1989 ◽  
Vol 64 (2) ◽  
pp. 557-569
Author(s):  
V T Fomenko ◽  
I A Bikchantaev
Keyword(s):  
Analytic Functions ◽  
Riemann Surfaces ◽  
Two Dimensional ◽  
Generalized Analytic Functions

Logarithmic Potential and Generalized Analytic Functions

2021 ◽  
Author(s):  
V. Gutlyanskiĭ ◽  
O. Nesmelova ◽  
V. Ryazanov ◽  
A. Yefimushkin
Keyword(s):  
Analytic Functions ◽  
Logarithmic Potential ◽  
Generalized Analytic Functions

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

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.).

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