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Comparison Finsler Geometry - 9783030806491
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Item specifics
- Condition
- Book Title
- Comparison Finsler Geometry
- ISBN
- 9783030806491
- Publication Year
- 2021
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Publication Name
- Comparison Finsler Geometry
- Item Height
- 235mm
- Publisher
- Springer Nature Switzerland A&G
- Item Width
- 155mm
- Subject
- Mathematics
- Item Weight
- 676g
- Number of Pages
- 316 Pages
About this product
Product Information
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-Weitzenboeck 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. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.
Product Identifiers
Publisher
Springer Nature Switzerland A&G
ISBN-13
9783030806491
eBay Product ID (ePID)
17049044766
Product Key Features
Publication Name
Comparison Finsler Geometry
Format
Hardcover
Language
English
Subject
Mathematics
Publication Year
2021
Type
Textbook
Number of Pages
316 Pages
Dimensions
Item Height
235mm
Item Width
155mm
Item Weight
676g
Additional Product Features
Series Title
Springer Monographs in Mathematics
Country/Region of Manufacture
Switzerland
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