Let γ n be the standard Gaussian measure on R n. We prove that for every symmetric convex
sets K, L in R n and every λ∈(0, 1), γ n (λ K+(1− λ) L) 1 n⩾ λ γ n (K) 1 n+(1− λ) γ n (L) 1 n …

We prove that ideal sub-Riemannian manifolds (ie, admitting no non-trivial abnormal
minimizers) support interpolation inequalities for optimal transport. A key role is played by …

The purpose of this work is to give a coherent introduction to the theory and methods behind
isoperimetric inequalities in Riemannian manifolds, including many of the results obtained in …

In 2011 Lutwak, Yang and Zhang extended the definition of the $ L_p $-Minkowski convex
combination ($ p\geq 1$) introduced by Firey in the 1960s from convex bodies containing …

In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies
when dealing with measures on the Euclidean space with either radially decreasing …

In this paper we address the following question: given a measure μ on R n, does there exist
a constant C> 0 such that, for any m-dimensional subspace H⊂ R n and any convex body …

We show that the lattice point enumerator G n (⋅) satisfies G n (t K+ s L+(− 1,⌈ t+ s⌉) n)
1/n≥ t G n (K) 1/n+ s G n (L) 1/n for any K, L⊂ R n bounded sets with integer points and all t …

We develop the framework of L p operations for functions: one based on an L p analogue of
the supremal convolution and another based on an L p analogue of the infimal convolution …

We construct the extension of the curvilinear summation for bounded Borel measurable sets
to the\(L_p\) space for multiple power parameter\(\bar {\alpha}=(\alpha _1,\ldots,\alpha _ {n+ …

In this paper we prove that the classical Brunn–Minkowski inequality holds for product
measures on the Euclidean space with quasi-convex densities when considering certain …