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Table of Contents
I Foundations of Finsler Geometry
1. Warm-up: Norms and inner products
2. Finsler manifolds
3. Properties of geodesics
4. Covariant derivatives
5. Curvature
6. Examples of Finsler manifolds
7. Variation formulas for arclength
8. Some comparison theorems
II Geometry and analysis of weighted Ricci curvature
9. Weighted Ricci curvature
10. Examples of measured Finsler manifolds
11. The nonlinear Laplacian
12. The Bochner-Weitzenbock formula
13. Nonlinear heat flow
14. Gradient estimates
15. Bakry-Ledoux isoperimetric inequality
16. Functional inequalities
III Further topics
17. Splitting theorems
18. Curvature-dimension condition
19. Needle decompositions.
1. Warm-up: Norms and inner products
2. Finsler manifolds
3. Properties of geodesics
4. Covariant derivatives
5. Curvature
6. Examples of Finsler manifolds
7. Variation formulas for arclength
8. Some comparison theorems
II Geometry and analysis of weighted Ricci curvature
9. Weighted Ricci curvature
10. Examples of measured Finsler manifolds
11. The nonlinear Laplacian
12. The Bochner-Weitzenbock formula
13. Nonlinear heat flow
14. Gradient estimates
15. Bakry-Ledoux isoperimetric inequality
16. Functional inequalities
III Further topics
17. Splitting theorems
18. Curvature-dimension condition
19. Needle decompositions.