Plane Lorentzian and Fuchsian Hedgehogs
Printed: Sep 2015
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).
Fuchsian and Lorentzian hedgehogs, evolute, duality, convolution, reversed isoperimetric inequality, reversed Bonnesen inequality
52A40 - Inequalities and extremum problems
52A55 - Spherical and hyperbolic convexity
53A04 - Curves in Euclidean space
53B30 - Lorentz metrics, indefinite metrics