Comparison Finsler Geometry

Language: English

Published by Springer, Springer International Publishing Okt 2022, 2022

3030806529 / 9783030806521

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 340 pp. Englisch.…

Seller Inventory # 9783030806521

Title
Comparison Finsler Geometry
Author
Shin-Ichi Ohta
Publisher
Springer, Springer International Publishing Okt 2022
Publication year
2022
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3030806529
ISBN 13
9783030806521
Item weight
517 grams
Dimensions
235x155x19 mm

buchversandmimpf2000

Emtmannsberg, BAYE, Germany

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