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Riemann surfaces

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Riemann surfaces [′rē‚män ‚sər·fə·səz]
(mathematics)
Sheets or surfaces obtained by analyzing multiple-valued complex functions and the various choices of principal branches.


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The text is intended to serve as a link between basic undergraduate geometry and more theoretical geometry such as Riemann surfaces, differential manifolds, algebraic topology, and Riemannian geometry.
Other subjects are string theory and knot invariants, quantum geometry of Riemann surfaces, and scaling algebras for charge carrying quantum fields and superselection structure at short distances.
The topics include Brownian motion and harmonic measure in conic sections, the sharpness of certain approach regions, integral representation for space-time excessive functions, hyperbolic Riemann surfaces without unbounded positive harmonic functions, and a vanishing theorem on the point- wise defect of a rational iteration sequence for moving targets.
 
 
 
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