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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Diffeomorphisms of the circle and hyperbolic curvature
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by David A. Singer
Conform. Geom. Dyn. 5 (2001), 1-5
DOI: https://doi.org/10.1090/S1088-4173-01-00066-2
Published electronically: February 21, 2001
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Abstract:

The trace $Tf$ of a smooth function $f$ of a real or complex variable is defined and shown to be invariant under conjugation by Möbius transformations. We associate with a convex curve of class $C^2$ in the unit disk with the Poincaré metric a diffeomorphism of the circle and show that the trace of the diffeomorphism is twice the reciprocal of the geodesic curvature of the curve. Then applying a theorem of Ghys on Schwarzian derivatives we give a new proof of the four-vertex theorem for closed convex curves in the hyperbolic plane.
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Bibliographic Information
  • David A. Singer
  • Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058
  • Email: das5@po.cwru.edu
  • Received by editor(s): July 26, 2000
  • Received by editor(s) in revised form: January 23, 2001
  • Published electronically: February 21, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 5 (2001), 1-5
  • MSC (2000): Primary 53A55; Secondary 52A55
  • DOI: https://doi.org/10.1090/S1088-4173-01-00066-2
  • MathSciNet review: 1836403