Ricci Curvature & Optimal Transport

Postgraduate Thesis uoadl:2921567 11 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2020-08-28
Year:
2020
Author:
Simos Sotirios
Supervisors info:
Παναγιώτης Γιαννιώτης, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Ricci Curvature & Optimal Transport
Languages:
English
Translated title:
Ricci Curvature & Optimal Transport
Summary:
After reminding some basic elements of Riemannian Geometry, we will make an introduction to the basics of optimal transport theory on Riemannian manifolds. The main result presented is the equivalence of a lower bound for Ricci curvature with the K-convexity of the relative entropy, a functional on the space of absolutely continuous (w.r.t. vol_g) probability measures. This equivalence allows the definition of lower Ricci bounds on metric measure spaces, where the Riemannian structure is absent.
Main subject category:
Science
Keywords:
ricci,curvature,optimal,transport,riemman,geometry,differential,manifold,manifolds,metric,measure,geodesic,geodesics,curve,curves,sectional,tensor
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
32
Number of pages:
98
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