Uniform convexity and smoothness,and their applications in Finsler geometry |
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Authors: | Shin-ichi Ohta |
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Institution: | (1) Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan |
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Abstract: | We generalize the Alexandrov–Toponogov comparison theorems to Finsler manifolds. Under suitable upper (lower, resp.) bounds
on the flag and tangent curvatures together with the 2-uniform convexity (smoothness, resp.) of tangent spaces, we show the
2-uniform convexity (smoothness, resp.) of Finsler manifolds. As applications, we prove the almost everywhere existence of
the second order differentials of semi-convex functions and of c-concave functions with the quadratic cost function. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 53C60 46B20 58C20 |
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