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EnglishWe 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.
| Autori: | |
| Titolo: | Sharp affine stability estimates for Hammer's problem |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.aam.2007.06.001 |
| Data di pubblicazione: | 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. |
| Lingua: | Inglese |
| Rivista: | |
| Citazione: | 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] |
| Appare nelle tipologie: | Articolo in rivista, Nota a sentenza |
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