Pairs of non-intersecting random flats
Let Ar, As,1≦r+s≦n-1, be independent isotropic uniform random r- resp. s-flats meeting a n-dimensional convex body K. It is shown that the probability that the points realizing the distance of Arand Asbelong to K is maximal if and only if K is a ball. © 1988 Springer-Verlag.
Guardado en:
| Autor principal: | |
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Springer-Verlag
1988
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | Let Ar, As,1≦r+s≦n-1, be independent isotropic uniform random r- resp. s-flats meeting a n-dimensional convex body K. It is shown that the probability that the points realizing the distance of Arand Asbelong to K is maximal if and only if K is a ball. © 1988 Springer-Verlag. |
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| Bibliografía: | Knothe, H., Über Ungleichungen bei Sehnenpotenzintegralen (1937) Deutsche Math., 2, pp. 544-551 Petkantschin, B., Zusammenhänge zwischen den Dichten der linearen Unterräume im n-dimensionalen Raum (1936) Abh. Math. Sem. Univ. Hamburg, 11, pp. 249-310 Santaló, L.A., (1976) Integral geometry and geometric probability, , Addison-Wesley, Reading, Mass Schneider, R., Inequalities for random flats meeting a convex body (1985) Journal of Applied Probability, 22, pp. 710-716 |
| ISSN: | 01788051 |
| DOI: | 10.1007/BF00319102 |