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Riemann mapping theorem

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  • Riemann mapping theorem — In complex analysis, the Riemann mapping theorem states that if U is a simply connected open subset of the complex number plane Bbb C which is not all of Bbb C, then there exists a biholomorphic (bijective and holomorphic) mapping f, from U, onto …   Wikipedia

  • Measurable Riemann mapping theorem — In the mathematical theory of quasiconformal mappings in two dimensions, the measurable Riemann mapping theorem, proved by Morrey (1936, 1938), generalizes the Riemann mapping theorem from conformal to quasiconformal homeomorphisms, and is… …   Wikipedia

  • Riemann-Roch theorem for smooth manifolds — In mathematics, a Riemann Roch theorem for smooth manifolds is a version of results such as the Hirzebruch Riemann Roch theorem or Grothendieck Riemann Roch theorem (GRR) without a hypothesis making the smooth manifolds involved carry a complex… …   Wikipedia

  • Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… …   Wikipedia

  • Riemann-Hilbert — For the original problem of Hilbert concerning the existence of linear differential equations having a given monodromy group see Hilbert s twenty first problem. In mathematics, Riemann Hilbert problems are a class of problems that arise, inter… …   Wikipedia

  • Mapping class group — In mathematics, in the sub field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of symmetries of the space. Contents 1 Motivation 2… …   Wikipedia

  • Riemann sphere — The Riemann sphere can be visualized as the complex number plane wrapped around a sphere (by some form of stereographic projection – details are given below). In mathematics, the Riemann sphere (or extended complex plane), named after the 19th… …   Wikipedia

  • Circle packing theorem — Example of the circle packing theorem on K5, the complete graph on five vertices, minus one edge. The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane …   Wikipedia

  • Bernhard Riemann — Infobox Scientist name =Bernhard Riemann box width =300px image width =225px caption =Bernhard Riemann, 1863 birth date =September 17, 1826 birth place =Breselenz, Germany death date =death date and age|1866|7|20|1826|9|17 death place =Selasca,… …   Wikipedia

  • Quasiconformal mapping — In mathematics, the concept of quasiconformal mapping, introduced as a technical tool in complex analysis, has blossomed into an independent subject with various applications. Informally, a conformal homeomorphism is a homeomorphism between plane …   Wikipedia

  • de Branges's theorem — In complex analysis, the Bieberbach conjecture or de Branges s theorem, posed by Ludwig Bieberbach (1916) and proven by Louis de Branges (1985), states a necessary condition on a holomorphic function to map the open unit disk of the… …   Wikipedia

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