| Abstract |
In this talk, we establish the Alexander-Bekelman-Pucci estimate, which is the maximum principle, for fully nonlinear nonlocal equations in a nondivergence form on the manifolds. In the first part, we deal with the manifold with nonnegative sectional curvature. In the second part, we deal with the hyperbolic space. In hyperbolic space, the behavior of the heat kernel is different from that on Euclidean space. Hence, in the ABP estimate, there is nonhomogeneous behavior. From these ABP estimates, we obtain robust Krylov-Safonov Harnack inequality.
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