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 concerning Euclidean and spherical cones (Bacher and Sturm [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 (Alexander and Bishop, 2004 [2]). For the proof we combine techniques developed in these papers. Because the Finslerian warped 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 space satisfying a curvature-dimension condition in the sense of Lott–Villani/Sturm.