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The Riemann Boundary Problem on Riemann Surfaces by Y. Rodin

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Published by Springer .
Written in English


  • Riemannian Manifolds,
  • Mathematics,
  • Science/Mathematics,
  • Calculus,
  • Mathematical Analysis,
  • Mathematics / Calculus,
  • Mathematics / Mathematical Analysis,
  • Mathematics-Mathematical Analysis,
  • Riemann surfaces,
  • Riemann-Hilbert problems

Book details:

Edition Notes

Mathematics and its Applications

The Physical Object
Number of Pages200
ID Numbers
Open LibraryOL9096805M
ISBN 109027726531
ISBN 109789027726537

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The Riemann Boundary Problem on Riemann Surfaces. Authors (view affiliations) Yu. L. Rodin; Book. 20 Search within book. Front Matter. Pages i-xiii The Riemann Boundary Problems for Vectors on Compact Riemann Surfaces. Yu. L. Rodin. Pages The Riemann Boundary Problem on Open Riemann Surfaces. Yu. L. Rodin. Pages E. Solvability of the Riemann Problem, 0. The Riemann Boundary Problem on Riemann Surfaces by Y. L. Rodin, , available at Book Depository with free delivery worldwide. Abstract. A Riemann surface is a two-dimensional manifold having a complex structure. We now define these notions. A two-dimensional manifold M is a Haussdorf topological space on which every point p ∈ M has a neighbourhoodU p homeomorphic to the unit disk |z| Cited by:

Finite Riemann surfaces are topologically completely characterized by the genus,, and the number of connected components of the boundary; their topological type is a sphere with handles and holes. In the normal form of a finite Riemann surface, the number of sides is not necessarily even, some sides corresponding to components of the boundary that remain free are not identified. $\begingroup$ I know Forster's book quite well, having taught out of a good portion of it a few times. It is extremely well-written, but definitely more analytic in flavor. In particular, it includes pretty much all the analysis to prove finite-dimensionality of sheaf cohomology on a compact Riemann surface. A Riemann problem, named after Bernhard Riemann, is a specific initial value problem composed of a conservation equation together with piecewise constant initial data which has a single discontinuity in the domain of interest. The Riemann problem is very useful for the understanding of equations like Euler conservation equations because all properties, such as shocks and rarefaction waves. A Riemann surface is a Riemannian manifold that is: 1) 2-dimensional, and 2) orientable. So, every Riemann surface is a Riemannian manifold, but not every Riemannian manifold is a Riemann surface. For example, a circle is a 1-dimensional Riemannia.

Other articles where Riemann surface is discussed: analysis: Analysis in higher dimensions: was the concept of a Riemann surface. The complex numbers can be viewed as a plane (see Fluid flow), so a function of a complex variable can be viewed as a function on the plane. Riemann’s insight was that other surfaces can also be provided with complex coordinates, and certain. The Riemann boundary value problem on closed Riemann surfaces and integrable systems: Authors: Rodin, Yu. L. Affiliation: AA(Institute of Solid State Physics of the Academy of the USSR, Chernogolovka, Moscow distr., , USSR) Publication: Physica D: Nonlinear Phenomena, Vol Issue , p. Publication Date: 01/ Origin: ELSEVIER. 10 CHAPTER 1. HOLOMORPHIC FUNCTIONS The second integral is defined for all z, and holomorphic in z. We write the first integral as Z1 0 tz−1(et−1)dt+ Z1 0 tz−1dt. Now the term Z 1. Samuel L. Krushkal, in Handbook of Complex Analysis, Teichmüller’s theory of extremal quasiconformal maps. In Teichmüller gave an extremely fruitful extension of the Grötzsch problem to the maps of Riemann surfaces of finite analytic type.. Recall that a Riemann surface X is a connected one-dimensional complex manifold, i.e., a topological surface endowed with a conformal.