The logarithmic Minkowski problem for non-symmetric measures

A flow method for the dual Orlicz–Minkowski problem

“…where c 2 is positive constant depending on ϕ C 2 (I [0,T ) ) , f C 2 (S n−1 ) and h C 1 (S n−1 ×[0,T )) and positive constants c 3 and c 4 depend on G C 2 (Ω [0,T ) ) . 15 From the definition of w,…”

Necessary subspace concentration conditions for the even dual Minkowski problem

“…For a related stability result concerning (1.8) we refer to [8]. In [15], Chen, Li and Zhu proved that also in the non-symmetric logarithmic Minkowski problem the subspace concentration condition is sufficient.…”

The 𝐿_{𝑝} Aleksandrov problem for origin-symmetric polytopes

“…A complete solution to the existence part of the logarithmic Minkowski problem, when restricting to even measures and the class of origin-symmetric convex bodies, was given by Böröczky-LYZ [11]. In the general case (non-even case), different efforts have been made by Böröczky, Hegedűs & Zhu [7], Stancu [46,47], Zhu [51], and most recently by Chen, Li & Zhu [15]. The logarithmic Minkowski problem has strong connections with isotropic measures (Böröczky-LYZ [12]) and curvature flows (Andrews [2,3]).…”