Sphere-preserving maps in inversive geometry

DOI10.1090/S0002-9939-01-06427-9zbMath0988.30005OpenAlexW1535206277MaRDI QIDQ2781244

David Minda, Alan F. Beardon

Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06427-9

zbMATH Keywords

cross-ratioMöbius transformationconformal mapcircle preserving mapsphere preserving map

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Reflection groups, reflection geometries (51F15)

Related Items (19)

On a rigidity problem of Beardon and Minda ⋮ Isometries in hyperbolic spaces ⋮ On characterizations of sphere-preserving maps ⋮ A new characteristic of Möbius transformations by use of polygons having type a ⋮ On the \(n\)-transitivity of the group of Möbius transformations on \(\mathbb{C}_{\infty}\) ⋮ A rigidity result for holomorphic quadratic differentials of finite norm in the unit disk ⋮ Geometric characterizations of symmetric maps in the complex plane ⋮ A quasiconformal analog of Carathéodory's criterion for the Möbius property of mappings ⋮ A four-point criterion for the Möbius property of a homeomorphism of plane domains ⋮ A geodesic-preserving map of a Euclidean cone disk is affine ⋮ Quasiconformality of the injective mappings transforming spheres to quasispheres ⋮ Geometric analysis on Cantor sets and trees ⋮ On the properties of sphere-preserving maps ⋮ The pseudo-affine transformations in \(\mathbb R^{2}\) ⋮ A new characteristic of Möbius transformations in hyperbolic geometry ⋮ Fundamental theorem of geometry without the surjective assumption ⋮ On existence of degenerate circle-preserving maps ⋮ Fundamental theorem of hyperbolic geometry without the injectivity assumption ⋮ Continued fractions, discrete groups and complex dynamics

Cites Work

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• Similarities and conformal transformations
• Spherical maps of euclidean spaces
• A new characteristic of Möbius transformations by use of Apollonius quadrilaterals
• Fundamental theorem of geometry without the 1-to-1 assumption
• On the characterization of plane projective and complex MOEBIUS‐transformations
• The most general transformations of plane regions which transform circles into circles

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