Functional versions of Lp-affine surface area and entropy inequalities Article

Caglar, U, Fradelizi, M, Guédon, O et al. (2016). Functional versions of Lp-affine surface area and entropy inequalities . INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016(4), 1223-1250. 10.1093/imrn/rnv151

cited authors

  • Caglar, U; Fradelizi, M; Guédon, O; Lehec, J; Schütt, C; Werner, EM

authors

abstract

  • In contemporary convex geometry, the rapidly developing Lp-Brunn-Minkowski theory is a modern analog of the classical Brunn-Minkowski theory. A central notion of this theory is the Lp-affine surface area of convex bodies. Here, we introduce a functional analog of this concept, for log-concave and s-concave functions. We show that the new analytic notion is a generalization of the original Lp-affine surface area. We prove duality relations and affine isoperimetric inequalities for log-concave and s-concave functions. This leads to a new inverse log-Sobolev inequality for s-concave densities.

publication date

  • January 1, 2016

published in

Digital Object Identifier (DOI)

start page

  • 1223

end page

  • 1250

volume

  • 2016

issue

  • 4