Heintze-Karcher Type Inequalities for Fractional GJMS Operators

In this paper, we genelize the Heintze-Karcher type inequalities for fractional Q-curvature $Q_{2\gamma }$ on conformally compact Einstein manifolds. Such inequality holds for all $\gamma \in (0,1]$. In particular, for $\gamma =\frac{1}{2}$ and $\gamma =1$, we obtain some rigidity theorems by characterising the equalities.