On the uniqueness of $L_p$-Minkowski problems: the constant $p$-curvature case in ${\mathbb{R}}^3$

Yong Huang, Jiakun Liu, Lu Xu

We study the $C^4$ smooth convex bodies $\mathbb{K}\subset {\mathbb{R}}^{n+1}$ satisfying $K(x)=u(x{)}^{1-p}$, where $x\in {\mathbb{S}}^n$, $K$ is the Gauss curvature of $\partial\mathbb{K…