ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

Tesi etd-06222017-005209


Tipo di tesi
Tesi di laurea magistrale
Autore
SEMOLA, DANIELE
URN
etd-06222017-005209
Titolo
An optimal transport approach to Lévy-Gromov inequality
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof. Ambrosio, Luigi
Parole chiave
  • Optimal transport
  • isoperimetric inequalities
  • curvature
  • localization
Data inizio appello
14/07/2017
Consultabilità
Completa
Riassunto
This thesis is devoted to the study of some applications of the so-called localization technique in the setting of compact Riemannian manifolds. The first appearance of this technique, essentially based on the reduction of an n-dimensional problem to a family of one dimensional problems, dates back to a work of Payne and Weinberger, where the authors proved a Poincaré-type inequality on convex domains of the Euclidean space by means of an iterative dimension reduction procedure.

We approach two different problems via localization techniques. The first one is the Monge transport problem for distance cost on Riemannian manifolds. The second one is the Lévy-Gromov isoperimetric inequality (and its infinite dimensional counterpart, namely the Bakry-Ledoux inequality). The bridge between these two results is given by the study of the localization properties of the so-called curvature-dimension condition.
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