The systematic study of harmonic self-maps on cohomogeneity one manifolds has recently been initiated by P\"uttmann and the second named author in \cite{MR4000241}. In this article we investigate corresponding Jacobi equation describing equivariant stability such self-maps. Besides several general statements concerning their explicitly solve for some cases spheres, special orthogonal groups $\S...

Abstract We study new examples of translating solitons the mean curvature flow, especially in Minkowski space. consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This general setting also covers classical Euclidean examples. As an application, we completely classify time-like, invariant rotations boosts