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 ?
He also uses Quillen's holomorphic theorem to evaluate the dependence of the determinants of the Laplace operations on the boundary conditions on the Riemann surface.
The proposal studies problems concerning the geometry and topology of moduli spaces of Higgs bundles on a Riemann surface motivated by parallel considerations in number theory and mathematical physics.
Hence if, conversely, a map A from a simply connected Riemann surface [summation] into ([h.
Another interesting instance is that of a Riemann surface endowed with the Poincare metric.
lambda]] and its natural domain of definition is the two-sheeted Riemann surface [R.
For any Riemann surface S of genus g [less than or equal to] 2,
s]/[partial]z are discontinuous on crossing the screen, and is taken into account in Sommerfeld's theory by "wrapping" the diffracting half plane in a semi-infinite, two-sided Riemann surface so that its positive and negative sides are distinguished by the values 2[pi] and 0 of the polar angle [PHI] in Fig.
We establish orthogonality on a generic closed contour on a Riemann surface.
4), if [omega] is allowed to range over the six sheets of its Riemann surface (2).
The description is based on an algebraic function of third degree and a harmonic function defined on the Riemann surface, which is associated with the algebraic function.
He presents the theory of Krichever-Nobikov algebras, Lax operator algebras, their interaction, elements of their representation theory, relations to moduli spaces of Riemann surface and holomorphic vector bundles of them and to Lax integrable systems and conformal field theory.
She won for her work on "the dynamics and geometry of Riemann surfaces and their moduli spaces.