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Second order analysis on $(\mathscr P_2(M),W_2)$

Author: Nicola Gigli
Journal: Memoirs of the AMS 216 (2012)
MSC (2000): Primary 53C15, 49Q20
Posted: June 21, 2011
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Abstract: We develop a rigorous second order analysis on the space of probability measures on a Riemannian manifold endowed with the quadratic optimal transport distance . Our discussion comprehends: definition of covariant derivative, discussion of the problem of existence of parallel transport, calculus of the Riemannian curvature tensor, differentiability of the exponential map and existence of Jacobi fields. This approach does not require any smoothness assumption on the measures considered.

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