03370nam 2200589 450 991048093760332120170816143308.00-8218-8529-4(CKB)3360000000464078(EBL)3114382(SSID)ssj0000889202(PQKBManifestationID)11478611(PQKBTitleCode)TC0000889202(PQKBWorkID)10874655(PQKB)10012351(MiAaPQ)EBC3114382(PPN)195419073(EXLCZ)99336000000046407820150416h20112011 uy 0engur|n|---|||||txtccrSecond order analysis on (P2(M),W2) /Nicola GigliProvidence, Rhode Island :American Mathematical Society,2011.©20111 online resource (154 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 216, Number 1018"March 2012, Volume 216, Number 1018 (end of volume)."0-8218-5309-0 Includes bibliographical references.""Contents""; ""Introduction""; ""Chapter 1. Preliminaries and notation""; ""1.1. Riemannian manifolds""; ""1.2. The distance W2""; ""1.3. Kantorovich's dual problem""; ""1.4. First order differentiable structure""; ""Chapter 2. Regular curves""; ""2.1. Cauchy Lipschitz theory on Riemannian manifolds""; ""2.2. Definition and first properties of regular curves""; ""2.3. On the regularity of geodesics""; ""Chapter 3. Absolutely continuous vector fields""; ""3.1. Definition and first properties""; ""3.2. Approximation of absolutely continuous vector fields""; ""Chapter 4. Parallel transport""""4.1. The case of an embedded Riemannian manifold""""4.2. Parallel transport along regular curves""; ""4.3. Forward and backward parallel transport""; ""4.4. On the question of stability and the continuity of P ""; ""Chapter 5. Covariant derivative""; ""5.1. Levi-Civita connection""; ""5.2. The tensor N""; ""5.3. Calculus of derivatives""; ""5.4. Smoothness of time dependent operators""; ""Chapter 6. Curvature""; ""6.1. The curvature tensor""; ""6.2. Related notions of curvature""; ""Chapter 7. Differentiability of the exponential map""; ""7.1. Introduction to the problem""""7.2. Rigorous result""""7.3. A pointwise result""; ""Chapter 8. Jacobi fields""; ""8.1. The Jacobi equation""; ""8.2. Solutions of the Jacobi equation""; ""8.3. Points before the first conjugate""; ""Appendix A. Density of regular curves""; ""Appendix B. C1 curves""; ""Appendix C. On the definition of exponential map""; ""Appendix D. A weak notion of absolute continuity of vector fields""; ""Bibliography""Memoirs of the American Mathematical Society ;Volume 216, Number 1018.Riemannian manifoldsGeometry, DifferentialSpaces of measuresElectronic books.Riemannian manifolds.Geometry, Differential.Spaces of measures.516.3/62Gigli Nicola227784MiAaPQMiAaPQMiAaPQBOOK9910480937603321Second order analysis on (P2(M),W2)2273271UNINA