Weighted Ricci curvature in Riemann-Finsler geometry

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Shen Zhongmin

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Journal Paper

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Journal: AUT Journal of Mathematics and Computing Year:2021 | Volume:2 | Issue:2 Page(s): 117-136

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Title

Weighted Ricci curvature in Riemann-Finsler geometry

Author(s)

Shen Zhongmin | Issue Writer Certificate

Keywords

Ricci curvature

S-curvature

Mean curvature

Abstract

Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the S-curvature, one can de, ne a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold. One can build up a bridge from Riemannian geometry to Finsler geometry via geodesic , elds. Then one can estimate the Laplacian of a distance function and the Mean curvature of a metric sphere under a lower weighted Ricci curvature by applying the results in the Riemannian setting. These estimates also give rise to a volume comparison of Bishop-Gromov type for Finsler metric measure manifolds.

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APA: Copy

Shen, Zhongmin. (2021). Weighted Ricci curvature in Riemann-Finsler geometry. AUT JOURNAL OF MATHEMATICS AND COMPUTING, 2(2), 117-136. SID. https://sid.ir/paper/1043867/en

Vancouver: Copy

Shen Zhongmin. Weighted Ricci curvature in Riemann-Finsler geometry. AUT JOURNAL OF MATHEMATICS AND COMPUTING[Internet]. 2021;2(2):117-136. Available from: https://sid.ir/paper/1043867/en

IEEE: Copy

Zhongmin Shen, “Weighted Ricci curvature in Riemann-Finsler geometry,” AUT JOURNAL OF MATHEMATICS AND COMPUTING, vol. 2, no. 2, pp. 117–136, 2021, [Online]. Available: https://sid.ir/paper/1043867/en

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