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 …

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 …

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 …

The $$L_p$$ -Gaussian Minkowski problem | Calculus of Variations and Partial Differential
Equations Skip to main content SpringerLink Account Menu Find a journal Publish with us …

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 …

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 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 …

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

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) …