To the families of geometric measures of convex bodies (the area measures of Aleksandrov‐
Fenchel‐Jessen, the curvature measures of Federer, and the recently discovered dual …

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 …

Employing a local version of the Brunn-Minkowski inequality, we give a new and simple
proof of a result due to Andrews, Choi and Daskalopoulos that the origin-centred balls are …

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 …

We will be concerned with the L p Gaussian Minkowski problem in Gaussian probability
space, which amounts to solving a class of Monge-Ampère type equations on the sphere. In …

The Lp-Brunn-Minkowski inequality for p < 1 - ScienceDirect Skip to main contentSkip to article
Elsevier logo Journals & Books Search RegisterSign in View PDF Download full issue Search …

We interpret the log-Brunn–Minkowski conjecture of Böröczky–Lutwak–Yang–Zhang as a
spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert …

Chord measures and L p chord measures were recently introduced by Lutwak-Xi-Yang-
Zhang by establishing a variational formula regarding a family of fundamental integral …

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