Geometry and Analysis on Finsler Spaces

Finsler geometry is a Riemannian geometry without quadratic restriction. It was originated from Riemann's ground-breaking 'Habilitation' address in the year 1854 and has many applications in many fields of the natural sciences including physics, psychology and ecology etc. The book is intended to provide basic materials on Finsler geometry for readers who are interested in Riemann-Finsler geometry, and to bring them into the frontiers of the active research on related topics.The book is comprised of three parts. The first part consists of Chapters 1-4, which cover the basic theory of Finsler geometry and important geometric invariants, including Riemannian quantities and non-Riemannian quantities. Chapters 5-6 present the theory of geodesics and comparison theorems, which are fundamental tools to investigate global Finsler geometry. The last part consisting of Chapters 7-9 presents the recent developments in the global analysis, including harmonic functions, the eigenvalue problem and heat flow etc., on Finsler manifolds although the problems discussed are classical.