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Tesi etd-02062013-201633


Thesis type
Tesi di dottorato di ricerca
Author
SCIENZA, MATTEO
URN
etd-02062013-201633
Title
Differentiability properties and characterization of H-convex functions
Settore scientifico disciplinare
MAT/05
Corso di studi
MATEMATICA
Commissione
tutor Prof. Magnani, Valentino
Parole chiave
  • stratified groups
  • h-convex
  • carnot group
Data inizio appello
15/02/2013;
Consultabilità
completa
Riassunto analitico
The present thesis deals with a number of geometric properties of convex functions in a non-Euclidean framework. This setting is represented by the so-called Sub-Riemannian space, also called a Carnot-Caratheodory (CC) space, that can be thought of as a space where the metric structure is a constrained geometry and one can move only along a prescribed set of directions depending on the point. We will study first order and second order reguarity of h-convex functions using h-subdifferentials. Moreover the distributional notion of h-convexity is considered. In this context we will prove that for all stratified groups an h-convex distribution is represented by an h-convex function. In the last chapter we address the study of convexity in general CC space. Here we prove a quantitative Lipschitz estimate for convex functions.
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