We prove that the area distance between two convex bodies K and K' with the same parallel X-rays in a set of n mutually non parallel directions is bounded from above by the area of their intersection, times a constant depending only on n. Equality holds if and only if K is a regular n-gon, and K' is K rotated by π/n about its center, up to affine transformations. This and similar sharp affine invariant inequalities lead to stability estimates for Hammer’s problem if the n directions are known up to an error, or in case X-rays emanating from n collinear points are considered. For n = 4, the order of these estimates is compared with the cross ratio of given directions and given points, respectively.

Peri, C., Dulio, P., Longinetti, M., Venturi, A., Sharp affine stability estimates for Hammer's problem, <<ADVANCES IN APPLIED MATHEMATICS>>, 2008; 41 (1): 27-51. [doi:10.1016/j.aam.2007.06.001] [http://hdl.handle.net/10807/36710]

Sharp affine stability estimates for Hammer's problem

Peri, Carla;Dulio, Paolo;
2008

Abstract

We prove that the area distance between two convex bodies K and K' with the same parallel X-rays in a set of n mutually non parallel directions is bounded from above by the area of their intersection, times a constant depending only on n. Equality holds if and only if K is a regular n-gon, and K' is K rotated by π/n about its center, up to affine transformations. This and similar sharp affine invariant inequalities lead to stability estimates for Hammer’s problem if the n directions are known up to an error, or in case X-rays emanating from n collinear points are considered. For n = 4, the order of these estimates is compared with the cross ratio of given directions and given points, respectively.
Inglese
Peri, C., Dulio, P., Longinetti, M., Venturi, A., Sharp affine stability estimates for Hammer's problem, <<ADVANCES IN APPLIED MATHEMATICS>>, 2008; 41 (1): 27-51. [doi:10.1016/j.aam.2007.06.001] [http://hdl.handle.net/10807/36710]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/36710
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