Abstract The Minkowski problem in Gaussian probability space is studied in this paper. In
addition to providing an existence result on a Gaussian-volume-normalized version of this …

The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular,
we show that if the Gaussian surface area measure is proportional to the spherical …

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 …

Abstract The Brunn-Minkowski theory in convex geometry concerns, among other things, the
volumes, mixed volumes, and surface area measures of convex bodies. We study …

The inequalities of Petty and Zhang are affine isoperimetric‐type inequalities providing
sharp bounds for Vol nn− 1 (K) Vol n (Π∘ K) \rmVol^n-1_n(K)\rmVol_n(Π^∘K), where Π K …

We prove that the (B) conjecture and the Gardner–Zvavitch conjecture are true for all log-
concave measures that are rotationally invariant, extending previous results known for …

The Brunn-Minkowski Theory has seen several generalizations over the past century. Many
of the core ideas have been generalized to measures. With the goal of framing these …

We study several of the recent conjectures in regards to the role of symmetry in the
inequalities of Brunn–Minkowski type, such as the L_p L p-Brunn–Minkowski conjecture of …

We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to $ n $
independent hyperplanes, and discuss the equality case and the uniqueness of the solution …

We prove that for any semi-norm on and any symmetric convex body in (1) and characterize
the equality cases of this new inequality. The above would also follow from the Log-Brunn …