Matheron's conjecture for the covariogram problem

• Autores: Gabriele Bianchi
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 71, Nº 1, 2005, págs. 203-220
• Idioma: inglés
• DOI: 10.1112/s0024610704006039
• Texto completo no disponible (Saber más ...)
• Resumen

  • The covariogram of a convex body provides the volumes of the intersections of with all its possible translates. Matheron conjectured in 1986 that this information determines among all convex bodies, up to certain known ambiguities. It is proved that this is the case if is not , or it is not strictly convex, or its boundary contains two arbitrarily small open portions 'on opposite sides'. Examples are also constructed that show that this conjecture is false in for any.