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Record Nr. |
UNINA9910788617603321 |
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Autore |
Gigli Nicola |
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Titolo |
Second order analysis on (P2(M),W2) / / Nicola Gigli |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2011 |
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©2011 |
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ISBN |
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Descrizione fisica |
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1 online resource (154 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 216, Number 1018 |
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Disciplina |
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Soggetti |
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Riemannian manifolds |
Geometry, Differential |
Spaces of measures |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"March 2012, Volume 216, Number 1018 (end of volume)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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. |
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