ArticleOriginal scientific text
Title
Étude des différences de corps convexes plans
Authors 1
Affiliations
- 1, rue Auguste Perret, F-92500 Rueil-Malmaison, France
Abstract
We characterize the linear space ℋ of differences of support functions of convex bodies of ² 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.
Keywords
Brunn-Minkowski theory, hedgehog, convex curve, support function
Bibliography
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- R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, 1993.
Pages:
71-78
Main language of publication
French
Received
1998-10-21
Accepted
1999-05-31
Published
1999
Exact and natural sciences