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Plane Lorentzian and Fuchsian Hedgehogs

Published online by Cambridge University Press:  20 November 2018

Yves Martinez-Maure
Yves Martinez-Maure*
Affiliation:
Institut Mathématique de Jussieu - Paris Rive Gauche, Bâtiment Sophie Germain, Case 7012, Paris Cedex 13, France e-mail: yves.martinez-maure@imj-prg.fr
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Abstract

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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 that are reversed as compared to classical ones).

Keywords

52A4052A5553A0453B30Fuchsian and Lorentzian hedgehogsevolutedualityconvolutionreversed isoperimetric inequalityreversed Bonnesen inequality
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 3 , 01 September 2015 , pp. 561 - 574
Copyright
Copyright © Canadian Mathematical Society 2015

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