Some new affine invariant stability results for the Hammer's problem.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.
STABILITÀ INVARIANTE PER AFFINITÀ PER IL PROBLEMA DI HAMMER- COMUNICAZIONE / P. DULIO ; M. LONGINETTI; C. PERI; A. VENTURI. - STAMPA. - (2006), pp. 1-25. (Intervento presentato al convegno MEETING GNAMPA: DISUGUAGLIANZE ANALITICHE E GEOMETRICHE IN CONVESSITÀ tenutosi a GAETA).
STABILITÀ INVARIANTE PER AFFINITÀ PER IL PROBLEMA DI HAMMER- COMUNICAZIONE
VENTURI, ADRIANA
2006
Abstract
Some new affine invariant stability results for the Hammer's problem.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.
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