Abstract
Comparison theorems are the main subjects of this book. They are concerned with quantitative or qualitative properties of a space with a certain condition on its curvature. In this book, we will consider Finsler manifolds whose flag or (weighted) Ricci curvature is bounded from below or above by a constant. This chapter is devoted to some fundamental examples of geometric comparison theorems. The first two of them (the Bonnet–Myers and Cartan–Hadamard theorems) are verbatim analogues of the Riemannian counterparts. Then we study the convexity and concavity of the distance function using some non-Riemannian quantities besides the flag curvature.
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Ohta, Si. (2021). Some Comparison Theorems. In: Comparison Finsler Geometry. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-80650-7_8
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DOI: https://doi.org/10.1007/978-3-030-80650-7_8
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