The $L_p$ Minkowski problem for $C$-close sets: existence and continuity

Wen Ai, Deping Ye, Baocheng Zhu

Let $C$ be a pointed closed convex cone in ${\mathbb{R}}^n$ with nonempty interior, and let $S^{n-1}$ denote the unit sphere in ${\mathbb{R}}^n$. The $L_p$ Minkowski problem for $C$-cl…