Planar Riemann surface information

In mathematics, a planar Riemann surface (or schlichtartig Riemann surface) is a Riemann surface sharing the topological properties of a connected open...

to prove the uniformization theorem and its generalization to planar Riemann surfaces. Later they supplied the analytic foundations for the harmonic...

Riemann matrix Riemann operator Riemann singularity theorem Riemann-Kempf singularity theorem Riemann surface Compact Riemann surface Planar Riemann surface...

In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number...

spaces by Riemann and led to what is known today as Riemannian geometry. The nineteenth century was the golden age for the theory of surfaces, from both...

geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this...

whose symmetry group equals their automorphism group as Riemann surfaces. The smallest Hurwitz surface is the Klein quartic (genus 3, automorphism group of...

of the rectangle and d − c is the height of the rectangle. Riemann could only use planar rectangles to approximate the area under the curve, because...

or the empty set and so that their union is a manifold. If a planar part of such a surface is not itself a convex polygon, O'Rourke requires it to be subdivided...

numbers, his most important results being on the uniformization of Riemann surfaces in a series of four papers in 1907–1909. He did his thesis at Berlin...

area of study in the work of Bernhard Riemann in his study of Riemann surfaces. Work in the spirit of Riemann was carried out by the Italian school of...

face of the polyhedral surface. By pulling the edges of the missing face away from each other, deform all the rest into a planar graph of points and curves...

a result of Osgood, Phillips, and Sarnak that the moduli space of Riemann surfaces of a given genus does not admit a continuous isospectral flow through...

× S 1 . {\displaystyle D^{2}\times S^{1}.} A Klein surface is, as for Riemann surfaces, a surface with an atlas allowing the transition maps to be composed...

Many theorems relating to planar conic sections also extend to spherical conics. If a sphere is intersected by another surface, there may be more complicated...

circle packing is a connected collection of circles (in general, on any Riemann surface) whose interiors are disjoint. The intersection graph of a circle packing...

determining the minimal surface of revolution, the surface of revolution of the planar curve between two given points which minimizes surface area. Solutions...

conjecture Hodge conjecture Navier–Stokes existence and smoothness P versus NP Riemann hypothesis Yang–Mills existence and mass gap The seventh problem, the Poincaré...

flat plane has constant curvature 0, these two surfaces are not isometric, not even locally. Thus any planar representation of even a small part of a sphere...

Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of higher dimensional spheres. Long studied for its...

products with a finite continued fraction Euler product formula for the Riemann zeta function. Euler–Maclaurin formula (Euler's summation formula) relating...

geometer Nikolai Lobachevsky. This page is mainly about the 2-dimensional (planar) hyperbolic geometry and the differences and similarities between Euclidean...