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math.DG2011
Applications of Toponogov's comparison theorems for open triangles
Kei Kondo, Minoru Tanaka
Recently we generalized Toponogov's comparison theorem to a complete Riemannian manifold with smooth convex boundary, where a geodesic triangle was replaced by an open (geodesic) t…
math.DG2011
The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces
Minoru Tanaka, Kei Kondo
We will construct surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comp…