Summary: Riemann­Finsler Geometry
MSRI Publications
Volume 49, 2004
Volumes on Normed and Finsler Spaces
J. C. ´ALVAREZ PAIVA AND A. C. THOMPSON
Contents
1. Introduction 1
2. A Short Review of the Geometry of Normed Spaces 3
2.1. Maps between normed spaces 5
2.2. Dual spaces and polar bodies 6
2.3. Sociology of normed spaces 7
3. Volumes on Normed Spaces 9
3.1. Examples of definitions of volume in normed spaces 10
3.2. The volume of the unit ball 13
3.3. Relationship between the definitions of volume 14
3.4. Extension to Finsler manifolds 15
4. k-Volume Densities 17
4.1. Examples of k-volume densities 18
4.2. Convexity of (n-1)-volume densities 20
4.3. Convexity properties of k-volume densities 26

Source: Alvarez, Juan Carlos - Department of Mathematics, Polytechnic University

Collections: Mathematics