Fixed Point Rigidity of the Operator ${\Gamma }_p{\Pi }_p^{\ast }$ and the LYZ Conjecture

Youjiang Lin, Sudan Xing

We characterize the fixed points of the operator ${\Gamma }_p{\Pi }_p^{\ast }$ for $n\ge 3$ and $1<p<n$. More precisely, we prove that a convex body $K\in {\mathcal{K}}_o^n$ satisfies \[Γ_pΠ_p^\ast K…