Some functional inverse Santaló inequalities

• Autores: Matthieu Fradelizi, M. Meyer
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 5, 2008, págs. 1430-1452
• Idioma: inglés
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• Resumen

  • Let be a log-concave function and for , define We discuss the problem of finding a sharp lower bound to the product We prove that if n=1, then P(f)e and characterize the case of equality. The same method allows to give a new simple proof of the fact that if f is sign-invariant, then for all n, P(f)4n. These inequalities are functional versions, with exact lower bounds, of the so-called inverse Santaló inequality for convex bodies, that we state and discuss as conjectures.