A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

Abstract We investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of operators, among which Pucci’s extremal some singular operators such as those modeled the p - $$\infty $$ ∞ -Laplacian, mean curvature-type problems. As byproduct, we establish new comparison uniformly elliptic problems when manifold has nonnegative sectional curvature.