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Name: Xia Q Geometry And Analysis On Finsler Spaces 2025
Format: pdf
Size: 8.74 MB

Title: Geometry and Analysis on Finsler Spaces (298 Pages)
Author: Qiaoling Xia
Language: polski
Year: 2025
Subjects: Science & Technology, Mathematics, Geometry, Geometry - General & Miscellaneous
Publisher: WSPC
ISBN: 9789811296697
Total pages: 299

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.
Qiaoling Xia is a professor at Hangzhou Dianzi University. Her main research field is differential geometry, Riemann-Finsler geometry and geometric analysis. She is currently engaging in the study of nonlinear analysis and topology on Finsler measure spaces and has made series of interesting results in recent years.