Abstract
We generalize the Alexandrov-Toponogov comparison theorem to the case of complete Riemannian manifolds referred to warped product models. We prove the maximal diameter theorem and the rigidity theorem. In particular, we discuss collapsing phenomena where the curvature explosion may occur.
Citation
Yukihiro Mashiko. Katsuhiro Shiohama. "Comparison geometry referred to warped product models." Tohoku Math. J. (2) 58 (4) 461 - 473, 2006. https://doi.org/10.2748/tmj/1170347684
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