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 …

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 …

In this paper, we study the existence of solutions to the centroaffine Minkowski problem,
namely the existence of closed convex hypersurfaces in the Euclidean space $\mathbb …

We introduce dual curvature measures for $\log $-concave functions, which in the case of
characteristic functions recover the dual curvature measures for convex bodies introduced …

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 …

Existence of Non-symmetric Solutions to the Gaussian Minkowski Problem | SpringerLink Skip
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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 …

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

Gaussian dual curvature measure is introduced and Gaussian dual Minkowski problem is
studied. This problem amounts to solving a class of Monge-Ampère type equations on the …