Étude des différences de corps convexes plans

Yves Martinez-Maure

Annales Polonici Mathematici (1999)

  • Volume: 72, Issue: 1, page 71-78
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Martinez-Maure, Yves. "Étude des différences de corps convexes plans." Annales Polonici Mathematici 72.1 (1999): 71-78. <http://eudml.org/doc/262794>.

@article{Martinez1999,
author = {Martinez-Maure, Yves},
journal = {Annales Polonici Mathematici},
keywords = {Brunn-Minkowski theory; hedgehog; convex curve; support function},
language = {fre},
number = {1},
pages = {71-78},
title = {Étude des différences de corps convexes plans},
url = {http://eudml.org/doc/262794},
volume = {72},
year = {1999},
}

TY - JOUR
AU - Martinez-Maure, Yves
TI - Étude des différences de corps convexes plans
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 1
SP - 71
EP - 78
LA - fre
KW - Brunn-Minkowski theory; hedgehog; convex curve; support function
UR - http://eudml.org/doc/262794
ER -

References

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  1. [1] H. Geppert, Über den Brunn-Minkowskischen Satz, Math. Z. 42 (1937), 238-254. Zbl0015.41001
  2. [2] M. Kallay, Reconstruction of a plane convex body from the curvature of its boundary, Israel J. Math. 17 (1974), 149-161. Zbl0285.52001
  3. [3] R. Langevin, G. Levitt et H. Rosenberg, Hérissons et multihérissons, dans : Singularities, Banach Center Publ. 20, PWN, Warszawa, 1988, 245-253. 
  4. [4] Y. Martinez-Maure, De nouvelles inégalités géométriques pour les hérissons, Arch. Math. (Basel) 72 (1999), 444-453. 
  5. [5] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, 1993. Zbl0798.52001

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