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Comparison Finsler Geometry (Springer Monographs in Mathematics) by Shin-ichi Ohta (auth.) is a nonfiction available to read on EtoBox.

What is Comparison Finsler Geometry (Springer Monographs in Mathematics) about?

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

Who reads Comparison Finsler Geometry (Springer Monographs in Mathematics)?

Author

Shin-ichi Ohta (auth.)

Publisher

Springer International Publishing : Imprint: Springer

Published

2021

Language

EN

ISBN

9783030806514

Category

nonfiction

Subjects

Mathematics, Geometry And Topology, Stem