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 nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and \(\infty \)-Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

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关于黎曼流形上完全非线性方程的强最大原理的一个注记

我们研究黎曼流形上完全非线性的二阶方程的强最大（和最小）原理，这些方程非完全退化并满足适当的缩放条件。我们的结果适用于一大类非线性算子，其中包括Pucci的极值算子，一些奇异算子，例如以p-和\（\ infty \）- Laplacian建模的算子，以及均值曲率型问题。作为副产品，当歧管具有非负截面曲率时，我们为一些二阶均匀椭圆问题建立了新的强比较原理。