Geometry And Analysis On Finsler Spaces
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A01=Qiaoling Xia
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Author_Qiaoling Xia
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Cartan Torsion
Category1=Non-Fiction
Category=PBK
Category=PBM
Chern Connection
Conjugate Point
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Eigenfunction
eq_isMigrated=0
eq_isMigrated=2
eq_nobargain
Exponential Map
Finsler Harmonic Function
Finsler Heat Flow
Finsler Laplacian
Finsler Manifold
First Eigenvalue
Flag Curvature
Gradient Estimate
Harnack Inequality
Jacobi Field
Language_English
Laplacian Comparison
Locally Projectively Flat
Minkowski Space
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Projectively Equivalent
PS=Forthcoming
Ricci Curvature
S-Curvature
Soblev Inequality etc.
softlaunch
Variation Formula
Volume Comparison
Weighted Ricci Curvature
Product details
- ISBN 9789811296673
- Publication Date: 24 Mar 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
- Language: English
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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.
