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Plane Lorentzian and Fuchsian Hedgehogs

  Published:2014-11-24
 Printed: Sep 2015
  • Yves Martinez-Maure,
    Institut Mathématique de Jussieu - Paris Rive Gauche, Bâtiment Sophie Germain, Case 7012, Paris Cedex 13, France
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Abstract

Parts of the Brunn-Minkowski theory can be extended to hedgehogs, which are envelopes of families of affine hyperplanes parametrized by their Gauss map. F. Fillastre introduced Fuchsian convex bodies, which are the closed convex sets of Lorentz-Minkowski space that are globally invariant under the action of a Fuchsian group. In this paper, we undertake a study of plane Lorentzian and Fuchsian hedgehogs. In particular, we prove the Fuchsian analogues of classical geometrical inequalities (analogues which are reversed as compared to classical ones).
Keywords: Fuchsian and Lorentzian hedgehogs, evolute, duality, convolution, reversed isoperimetric inequality, reversed Bonnesen inequality Fuchsian and Lorentzian hedgehogs, evolute, duality, convolution, reversed isoperimetric inequality, reversed Bonnesen inequality
MSC Classifications: 52A40, 52A55, 53A04, 53B30 show english descriptions Inequalities and extremum problems
Spherical and hyperbolic convexity
Curves in Euclidean space
Lorentz metrics, indefinite metrics
52A40 - Inequalities and extremum problems
52A55 - Spherical and hyperbolic convexity
53A04 - Curves in Euclidean space
53B30 - Lorentz metrics, indefinite metrics
 

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