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Tesi etd-05242016-104637


Thesis type
Tesi di laurea magistrale
Author
PIGATI, ALESSANDRO
URN
etd-05242016-104637
Title
New regularity results for sub-Riemannian geodesics
Struttura
MATEMATICA
Corso di studi
MATEMATICA
Supervisors
relatore Prof. Ambrosio, Luigi
relatore Prof. Vittone, Davide
controrelatore Prof. Magnani, Valentino
Parole chiave
  • Goh conditions
  • Hakavuori-Le Donne theorem
  • Liu-Sussmann minimality theorem
  • normal and abnormal extremals
  • Sub-Riemannian manifolds
  • Chow-Rashevsky theorem
  • Carnot groups
Data inizio appello
10/06/2016;
Consultabilità
Completa
Riassunto analitico
After a brief introduction to sub-Riemannian manifolds, we give a first order classification of geodesics, which can be normal or abnormal, as well as the second order Goh conditions. Explicit examples of strictly abnormal minimizers are provided, using a result by Liu-Sussmann.
We examine closely the model case of Carnot groups, reviewing here a new result by Hakavuori-Le Donne which excludes corner-like singularities. Finally, we obtain an interesting quantitative refinement, which excludes a wider class of singularities in Carnot groups of rank 2.
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