- Singular Sets of Generalized Convex Functions

- Penso, Valentina <1988>

- MAT/05 Analisi matematica

- In the first part of the dissertation we prove that, under quite general conditions on a cost function $c$ in $\RR^n$, the Hausdorff dimension of the singular set of a $c$-concave function has dimension at most $n-1$. Our result applies for non-semiconcave cost functions and has applications in optimal mass transportation. The purpose of the second part of the thesis is to extend a result of Alberti and Ambrosio about singularity sets of monotone multivalued maps to the sub-Riemannian setting of Heisenberg groups. We prove that the $k$-th horizontal singular set of a $H$-monotone multivalued map of the Heisenberg group $\HH^n$, with values in $\RR^{2n}$, has Hausdorff dimension at most $2n+2-k$.

- 2017-05-09

- Doctoral Thesis

- PeerReviewed

- application/pdf

urn:nbn:it:unibo-20835

Penso, Valentina (2017) Singular Sets of Generalized Convex Functions, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica