Browsing by Subject "Log concave functions"
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- PublicationOpen AccessFurther inequalities for the (generalized) Wills functional(World Scientific Publishing, 2020-03-05) Alonso Gutiérrez, David ; Yepes Nicolás, Jesús; Hernández Cifre, María de los Ángeles; Matemáticas; Facultades de la UMU::Facultad de MatemáticasThe Wills functional 𝒲(K) of a convex body K, defined as the sum of its intrinsic volumes Vi(K), turns out to have many interesting applications and properties. In this paper, we make profit of the fact that it can be represented as the integral of a log-concave function, which, furthermore, is the Asplund product of other two log-concave functions, and obtain new properties of the Wills functional (indeed, we will work in a more general setting). Among others, we get upper bounds for 𝒲(K) in terms of the volume of K, as well as Brunn–Minkowski and Rogers–Shephard-type inequalities for this functional. We also show that the cube of edge-length 2 maximizes 𝒲(K) among all 0-symmetric convex bodies in John position, and we reprove the well-known McMullen’s inequality 𝒲(K) ≤ e^{V1(K)} using a different approach.