Étude des différences de corps convexes plans

• Autorzy: Yves Martinez-Maure
• Języki publikacji: FR

Abstrakty

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.

Słowa kluczowe

EN

Brunn-Minkowski theory   hedgehog   convex curve   support function  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1999
• Tom: 72
• Numer: 1
• Strony: 71-78

Daty

wydano

1999

otrzymano

1998-10-21

poprawiono

1999-05-31

Twórcy

autor

Yves Martinez-Maure

• 1, rue Auguste Perret, F-92500 Rueil-Malmaison, France

Bibliografia

• [1] H. Geppert, Über den Brunn-Minkowskischen Satz, Math. Z. 42 (1937), 238-254.
• [2] M. Kallay, Reconstruction of a plane convex body from the curvature of its boundary, Israel J. Math. 17 (1974), 149-161.
• [3] R. Langevin, G. Levitt et H. Rosenberg, Hérissons et multihérissons, dans : Singularities, Banach Center Publ. 20, PWN, Warszawa, 1988, 245-253.
• [4] Y. Martinez-Maure, De nouvelles inégalités géométriques pour les hérissons, Arch. Math. (Basel) 72 (1999), 444-453.
• [5] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, 1993.