Riemann Surface

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Riemann Surface

 

one of the basic concepts of the theory of functions of a complex variable. The Riemann surface was introduced by B. Riemann in 1851 for the purpose of replacing the study of multiple-valued analytic functions by the study of single-valued analytic functions of a point on corresponding Riemann surfaces (seeANALYTIC FUNCTIONS).

References in periodicals archive ?
n] of linear differential operators on sections of V is called a conformally invariant system if, for each X [member of] g, there are smooth functions [C.
A typical example for a conformally invariant system of one differential operator is the wave operator [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on the Minkowski space [R.
The notion of conformally invariant systems generalizes that of quasi-invariant differential operators introduced by Kostant in [12] and is related to a work of Huang ([9]).
1) is that the common kernel of the operators in the conformally invariant system [D.
Although the theory of conformally invariant systems can be viewed as a geometric-analytic theory, it is also closely related to algebraic objects such as generalized Verma modules.
0] if the system is conformally invariant on the line bundle [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
a) If V([mu] + [epsilon]) is of type 1a then the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] system is conformally invariant on [L.
1) Eun-Seo Choi, Certain conformally invariant connections of Rizza mani- folds, Commun.
US and European mathematicians offer some new perspectives on the algebras, which were devised as a mathematically rigorous formulation of the physical theory of conformally invariant quantum field theories in two dimensions, and has now grown into a major research area.
LAWLER, Conformally Invariant Processes in the Plane, American Mathematical Society, Providence, RI, 2005.
Conformally invariant systems of differential operators associated to maximal parabolics of quasi-Heisenberg type Toshihisa KUBO Communicated by Kenji FUKAYA, M.
Lawler introduces integration with respect to Brownian motion and continuous semimartingales, explains the Loewner differential equation, derives conformally invariant measures on paths from complex Brownian motion, and analyzes the Loewner differential equation driven by Brownian motion.