Comparison Finsler geometry / Shin-ichi Ohta.
Ohta, Shin-ichi, author.
2021
QA689 .O48 2021
Available Online

Linked e-resources

Linked Resource Online Access
Concurrent users Unlimited
Authorized users Authorized users
Document Delivery Supplied Can lend chapters, not whole ebooks

Details

Title Comparison Finsler geometry / Shin-ichi Ohta.
Author Ohta, Shin-ichi, author.
ISBN 9783030806507 (electronic bk.)
3030806502 (electronic bk.)
9783030806491
3030806499
DOI https://doi.org/10.1007/978-3-030-80650-7
Published Cham : Springer, [2021]
Copyright ©2021
Language English
Description 1 online resource : illustrations
Item Number 10.1007/978-3-030-80650-7 doi
Call Number QA689 .O48 2021
Dewey Decimal Classification 516.3/75
Summary 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. 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed October 18, 2021).
Series Springer monographs in mathematics. 2196-9922
Available in Other Form Comparison Finsler geometry.
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
All Resources
I Foundations of Finsler Geometry
1. Warm-up: Norms and inner products
2. Finsler manifolds
3. Properties of geodesics
4. Covariant derivatives
5. Curvature
6. Examples of Finsler manifolds
7. Variation formulas for arclength
8. Some comparison theorems
II Geometry and analysis of weighted Ricci curvature
9. Weighted Ricci curvature
10. Examples of measured Finsler manifolds
11. The nonlinear Laplacian
12. The Bochner-Weitzenbock formula
13. Nonlinear heat flow
14. Gradient estimates
15. Bakry-Ledoux isoperimetric inequality
16. Functional inequalities
III Further topics
17. Splitting theorems
18. Curvature-dimension condition
19. Needle decompositions.

Browse Subjects

Show more subjects...

Statistics

from
to
Export