4 papers
On stochastic forms of functional isoperimetric inequalities
Francisco Marín Sola
We present a probabilistic interpretation of several functional isoperimetric inequalities within the class of -concave functions, building on random models for such functions i…
Grünbaum's inequality for Gaussian and convex probability measures
Matthieu Fradelizi, Dylan Langharst, Jiaqian Liu +2
A celebrated result in convex geometry is Grünbaum's inequality, which quantifies how much volume of a convex body can be cut off by a hyperplane passing through its barycenter. In…
Entropy, slicing problem and functional Mahler's conjecture
Matthieu Fradelizi, Francisco Marín Sola
In a recent work, Bo'az Klartag showed that, given a convex body with minimal volume product, its isotropic constant is related to its volume product. As a consequence, he obtained…
Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions
Dylan Langharst, Francisco Marín Sola, Jacopo Ulivelli
The Rogers-Shephard and Zhang's projection inequalities are two reverse, affine isoperimetric-type inequalities for convex bodies. Following a classical work by Schneider, both ine…