| 书目名称 | Comparison Finsler Geometry |
| 编辑 | Shin-ichi Ohta |
| 视频video | http://file.papertrans.cn/232/231042/231042.mp4 |
| 概述 | Generalizes the weighted Ricci curvature and develops comparison geometry and geometric analysis in the Finsler context.Offers an accessible entry point to studying Finsler geometry for those familiar |
| 丛书名称 | Springer Monographs in Mathematics |
| 图书封面 |  |
| 描述 | .This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area...Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Througho |
| 出版日期 | Book 2021 |
| 关键词 | Finsler geometry; Finsler manifolds; Introduction to Finsler geometry; Comparison geometry in Finsler c |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-80650-7 |
| isbn_softcover | 978-3-030-80652-1 |
| isbn_ebook | 978-3-030-80650-7Series ISSN 1439-7382 Series E-ISSN 2196-9922 |
| issn_series | 1439-7382 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
|Archiver|手机版|小黑屋|
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