We obtain Harnack estimates for a class of curvature flows in Riemannian manifolds of constant nonnegative sectional curvature as well as in the Lorentzian Minkowski and de Sitter spaces. Furthermore, we prove a Harnack estimate with a bonus term for mean curvature flow in locally symmetric Riemannian Einstein manifolds of nonnegative sectional curvature. Using a concept of “duality” for strictly convex hypersurfaces, we also obtain a new type of inequality, so-called “pseudo”-Harnack inequality, for expanding flows in the sphere and in the hyperbolic space.

中文翻译：

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黎曼流形和洛伦兹流形中曲率流的Harnack不等式

我们获得具有恒定非负截面曲率的黎曼流形中的一类曲率流以及Lorentzian Minkowski和de Sitter空间中的一类曲率流的Harnack估计。此外，我们证明了具有非负截面曲率的局部对称黎曼爱因斯坦流形中的平均曲率流的加分项的Harnack估计。使用严格凸超曲面的“对偶性”概念，我们还获得了一种新型的不等式，即所谓的“伪” -Harnack不等式，用于扩展球面和双曲空间中的流动。