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- W1696075560 abstract "The trace <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper T f> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>Tf</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of a smooth function <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C squared> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>C^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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." @default.
- W1696075560 created "2016-06-24" @default.
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- W1696075560 date "2001-02-21" @default.
- W1696075560 modified "2023-10-03" @default.
- W1696075560 title "Diffeomorphisms of the circle and hyperbolic curvature" @default.
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- W1696075560 doi "https://doi.org/10.1090/s1088-4173-01-00066-2" @default.
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