Ricci Curvature Bounds for Warped Products

We prove generalized lower Ricci curvature bounds for warped products over complete Finsler manifolds. On the one hand our result covers a theorem of Bacher and Sturm con-cerning euclidean and spherical cones ([3]). On the other hand it can be seen in analogy to a result of Bishop and Alexander in the setting of Alexandrov spaces with curvature bounded from below ([1]). For the proof we combine techniques developed in these papers. Because the Finslerian product metric can degenerate we regard a warped product as metric measure space that is in general neither a Finsler manifold nor an Alexandrov space again but a spac