Projection problems for symmetric polytopes

• Autores: Binwu Hen, Leng Gangsong, Kanghai Li
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 1, 2006, págs. 73-90
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.11.006
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• Resumen

  • Let be a convex body (a compact, convex subset with non-empty interior), ?K its projection body. Finding the least upper bound, as K ranges over the class of origin-symmetric convex bodies, of the affine-invariant ratio V(?K)/V(K)n-1, being called Schneider's projection problem, is a well-known open problem in the convex geometry. To study this problem, Lutwak, Yang and Zhang recently introduced a new affine invariant functional for convex polytopes in . For origin-symmetric convex polytopes, they posed a conjecture for the new functional U(P). In this paper, we give an affirmative answer to the conjecture in , thereby, obtain a modified version of Schneider's projection problem.