Title: Toponogov's triangle comparison theorem in model spaces of nonconstant curvature
Abstract: So far there exist two versions of Toponogov's triangle comparison theorem with surfaces of revolution as model spaces. U. Abresch has considered surfaces of nonpositive curvature and D. Elerath has investigated embedded surfaces of positive curvature. As the classical theorem, these two extensions are proved applying Rauch's comparison theorems. In this paper we present a new version of Toponogov's theorem generalizing all comparison theorems mentioned above. The new proof is based on estimates for the second fundamental tensor of distance spheres and handles the rigidity as well.