Heintze-Karcher Type Inequalities of Fractional GJMS Operators

In this paper, we genelize the Heintze-Karcher type inequalities for fractional Q-curvature Q2γ on conformally compact Einstein manifolds. Such inequality holds for all γ∈ (0,1]. In particular, for γ=1/2 and γ=1, we obtain some rigidity theorems by characterising the equalities. Moreover, we also verify the Heintze-Karcher inequality on Riemannian manifolds with sectional curvature bounded below.