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Étude des différences de corps convexes plans

100%
Martinez-Maure Y.
Annales Polonici Mathematici
|
1999
|
tom 72
|
nr 1
71-78
EN
We characterize the linear space ℋ of differences of support functions of convex bodies of 𝔼² and we consider every h ∈ ℋ as the support function of a generalized hedgehog (a rectifiable closed curve having exactly one oriented support line in each direction). The mixed area (for plane convex bodies identified with their support functions) has a symmetric bilinear extension to ℋ which can be interpreted as a mixed area for generalized hedgehogs. We study generalized hedgehogs and we extend the Minkowski inequality.
2
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Uniqueness results for the Minkowski problem extended to hedgehogs

100%
Martinez-Maure Y.
Open Mathematics
|
2012
|
tom 10
|
nr 2
440-450
EN
The classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere $\mathbb{S}^n $ of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.
3
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Hedgehogs of constant width and equichordal points

100%
Martinez-Maure Y.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 3
285-288
EN
We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.
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