# Second Order Analysis on \((\mathscr{P}_{2}(M),W_{2})\)

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*Nicola Gigli*

#### Table of Contents

# Table of Contents

## Second Order Analysis on $(\mathscr{P}_{2}(M),W_{2})$

- Introduction vii8 free
- Chapter 1. Preliminaries and notation 114 free
- Chapter 2. Regular curves 2134
- Chapter 3. Absolutely continuous vector fields 3952
- Chapter 4. Parallel transport 4962
- Chapter 5. Covariant derivative 6578
- Chapter 6. Curvature 93106
- Chapter 7. Differentiability of the exponential map 101114
- Chapter 8. Jacobi fields 113126
- Appendix A. Density of regular curves 121134
- Appendix B. C1 curves 131144
- Appendix C. On the definition of exponential map 139152
- Appendix D. A weak notion of absolute continuity of vector fields 147160
- Bibliography 153166