Information om | Engelska ordet QUASICONFORMAL

Exempel på hur man kan använda QUASICONFORMAL i en mening

• He introduced quasiconformal mappings and differential geometric methods into the study of Riemann surfaces.
• Interactions with the theory of quasiconformal analysis on metric spaces, particularly in relation to Cannon's conjecture about characterization of hyperbolic groups with Gromov boundary homeomorphic to the 2-sphere.
• Moreover, it also follows from the theory of quasiconformal mappings that two compact Riemann surfaces are diffeomorphic if and only if they are homeomorphic.
• A quasiconformal mapping between two Riemann surfaces is a homeomorphism which deforms the conformal structure in a bounded manner over the surface.
• If K > 1 then the maps x + iy ↦ Kx + iy and x + iy ↦ x + iKy are both quasiconformal and have constant dilatation K.
• In the case of the unit disk, Teichmüller theory implies that the homomorphism carries quasiconformal homeomorphisms of the disk onto the group of quasi-Möbius homeomorphisms of the circle (using for example the Ahlfors–Beurling or Douady–Earle extension): it follows that the homomorphism from the quasi-isometry group into the quasi-Möbius group is surjective.
• The Connes–Donaldson–Sullivan–Teleman index theorem is an extension of the Atiyah–Singer index theorem to quasiconformal manifolds due to a joint paper by Simon Donaldson and Sullivan in 1989 and a joint paper by Alain Connes, Sullivan, and Nicolae Teleman in 1994.
• Thus a closed Riemannian 2-manifold of non-positive curvature can never be embedded isometrically in ; however, as Adriano Garsia showed using the Beltrami equation for quasiconformal mappings, this is always possible for some conformally equivalent metric.
• Morrey worked on numerous fundamental problems in analysis, among them, the existence of quasiconformal maps, the measurable Riemann mapping theorem, Plateau's problem in the setting of Riemannian manifolds, and the characterization of lower semicontinuous variational problems in terms of quasiconvexity.

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