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 …

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 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 …

Let be a smooth, origin-symmetric, strictly convex body in. If for some, the anisotropic
Riemannian metric, encapsulating the curvature of, is comparable to the standard Euclidean …

ThecurrentstateoftheartconcerningtheLp-MinkowskiproblemasaMonge–Ampère equation on
the sphere and Lutwak's logarithmic Minkowski conjecture about …

For fixed positive integer n, p∈[0, 1), a∈(0, 1), we prove that if a function g: S n-1→ R is
sufficiently close to 1, in the C a sense, then there exists a unique convex body K whose L p …

We establish a sharp upper-bound for the first non-zero eigenvalue corresponding to an
even eigenfunction of the Hilbert–Brunn–Minkowski operator (the centro-affine Laplacian) …

We formulate a plausible conjecture for the optimal Ehrhard-type inequality for convex
symmetric sets with respect to the Gaussian measure. Namely, letting $ J_ {k-1}(s)=\int^ s_0 …