Geometry and Analysis on Finsler Spaces, VOL 17

Geometry and Analysis on Finsler Spaces, VOL 17 | 36.86 MB

Title: Geometry and Analysis on Finsler Spaces
Author: Qiaoling Xia
Category: Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Geometry
Language: English | 222 Pages | ISBN: 9789811296697

Description:
Finsler geometry is just Riemannian geometry without a quadratic restriction. It has applications in many fields of natural sciences, including physics, psychology, and ecology. The book is intended to provide basic materials on Finsler geometry for readers and to bring them to the frontiers of active research on related topics.
This book is comprised of three parts. In Part I (Chapters 1–4), the author introduces the basics, such as Finsler metrics, the Chern connection, geometric invariant quantities, etc., and gives some rigidity results on Finsler manifolds with certain curvature properties. Part II (Chapters 5–6) covers the theory of geodesics, using which the author establishes some comparison theorems, which are fundamental tools to study global Finsler geometry. In Part III (Chapters 7–9), the author presents recent developments in nonlinear geometric analysis on Finsler spaces, partly based on the author's recent works on Finsler harmonic functions, the eigenvalue problem, and heat flow. The author has made efforts to ensure that the contents are accessible to advanced undergraduates, graduate students, and researchers who are interested in Finsler geometry.
Contents:

• Minkowski Spaces
  
• Finsler Manifolds
  
• Connections and Structure Equations
  
• Curvature Invariant Quantities
  
• Theory of Geodesics
  
• Comparison Theorems
  
• Finsler Harmonic Functions
  
• The Eigenvalue Problem
  
• Heat Flow on Finsler Manifolds
  
• Appendix: Sobolev Spaces on Compact Finsler Manifolds
  

Readership: Graduates or researchers interested in differential geometry, especially Riemannian–Finsler geometry.

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