$Second Order Analysis on $(/mathscr{P}_2(M),W_2)$ - Nicola Gigli$

Second Order Analysis on $(/mathscr{P}_2(M),W_2)$

Nicola Gigli (Autor)

Buch | Softcover

154 Seiten

2012
American Mathematical Society (Verlag)
978-0-8218-5309-2 (ISBN)

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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.

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-5309-0 / 0821853090
ISBN-13	978-0-8218-5309-2 / 9780821853092
Zustand	Neuware