Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Too long shadow boundaries

Author: Tudor Zamfirescu
Journal: Proc. Amer. Math. Soc. 103 (1988), 587-590
MSC: Primary 52A20; Secondary 54E52
MathSciNet review: 943088
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that, in the sense of Baire categories, most $ d$-dimensional convex bodies have infinitely long shadow boundaries if the light comes along one of many $ \left( {d - 2} \right)$-dimensional subspaces. This reveals (once again!) a striking contrast between the categorical and the measure-theoretical points of view.

References [Enhancements On Off] (What's this?)

  • [1] P. Gruber, Die meisten konvexen Körper sind glatt, aber nicht zu glatt, Math. Ann. 229 (1977), 259-266. MR 0442825 (56:1202)
  • [2] V. Klee, Some new results on smoothness and rotundity in normed linear spaces, Math. Ann. 139 (1959), 51-63. MR 0115076 (22:5879)
  • [3] D. G. Larman and P. Mani, Almost all shadow boundaries are almost smooth, manuscript.
  • [4] P. Steenaerts, Mittlere Schattengrenzenlänge konvexer Körper, Results in Math. 8 (1985), 54-77. MR 812246 (87d:52007)
  • [5] T. Zamfirescu, Using Baire categories in geometry, Rend. Sem. Mat. Univ. Politec. Torino 43 (1985), 67-88. MR 859850 (87j:52007)
  • [6] -, Nearly all convex bodies are smooth and strictly convex, Monatsh. Math. 103 (1987), 57-62. MR 875352 (88b:52007)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 52A20, 54E52

Retrieve articles in all journals with MSC: 52A20, 54E52

Additional Information

Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society