Plane Lorentzian and Fuchsian hedgehogs

Yves Martinez-Maure (1)

1 IMJ - Institut de Mathématiques de Jussieu

Parts of the Brunn-Minkowski theory can be extended to hedgehogs, which are envelopes of families of affine hyperplanes parametrized by their Gauss map. In [F], 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).

Mots clés: Fuchsian and Lorentzian hedgehogs; evolute; duality; convolution; reversed isoperimetric inequality; reversed Bonnesen inequality

Domaines: Géométrie différentielle [math.DG]

Yves Martinez-Maure. Plane Lorentzian and Fuchsian hedgehogs. 2014. ⟨hal-01054386⟩