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The infinite-Laplace equation and the distance function in Riemannian and sub-Riemannian manifolds

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Giovedi' 15 aprile in aula 2BC/30 alle ore 12.00 Federica Dragoni (University of Bristol) terra' un seminario dal titolo "The infinite-Laplace equation and the distance function in Riemannian and sub-Riemannian manifolds".

-Abstract
A simple computation shows that the Euclidean distance from the origin is infinite-harmonic in R^n away from the origin. Is the same true in Riemannian and sub-Riemannian manifolds? We found a characterization by geodesics for the set where the distance function is infinite-harmonic. The key point is the equivalence between Absolutely Minimizing Lipschitz Extension and infinite-harmonic functions. This equivalence was already known in Euclidean spaces and Carnot groups and has been recently proved in general Riemannian and sub-Riemannian manifolds. In the particular case of the Heisenberg group, we can explicitly prove that the Carnot-Caratheodory distance is not infinite-harmonic in the center of the group.

Rif. int. M. Bardi, A. Cesaroni, M. Novaga, D. Vittone

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