Uniqueness when the $L_p$ curvature is close to be a constant for $p\in [0,1)$

Károly J. Böröczky, Christos Saroglou

For fixed positive integer $n$, $p\in [0,1]$, $a\in (0,1)$, we prove that if a function $g:{\mathbb{S}}^{n-1}\to \mathbb{R}$ is sufficiently close to 1, in the $C^a$ sense, then there…