Second Order Analysis on P2m, W2

(Memoirs of the American Mathematical Society)

5c0cddb1ee735.jpg Author Nicola Gigli
Isbn 9780821853092
File size 1.28MB
Year 2012
Pages 154
Language English
File format PDF
Category Mathematics

Book Description:

The author develops a rigorous second order analysis on the space of probability measures on a Riemannian manifold endowed with the quadratic optimal transport distance $W_2$. The discussion includes: 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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