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In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, whichnot only generalizes Schur's and Toponogov's theorem but also indicates theirrelation. Inspired by its proof, we also supply a new proof of Toponogov'stheorem (in the large) in Alexandrov geometry.

A Schur-Toponogov theorem in Riemannian geometry & a new proof of Toponogov's theorem in Alexandrov geometry