“Graphs of prescribed mean curvature in Heisenberg groups”
Martedì 14 Maggio 2024, ore 17:00 - Aula 2AB40 - Julian Pozuelo Dominguez (PostDoc Università di Padova)
Abstract
This talk is devoted to the prescribed mean curvature equation for t-graphs in a Riemannian Heisenberg group. Following results due to Giusti, we will prove existence of BV solutions in the so-called non-extremal domains without imposing Dirichlet conditions. Then the regularity will be improved in consecutive steps to obtain classical solutions in this domains.
The main goal of the talk are the characterization of the existence of classical solutions of the equation and the study of several conditions that implies the uniqueness of them. Finally, by an approximation technique, we obtain solutions to the sub-Riemannian prescribed mean curvature equation.
This result are obtained in collaboration with S. Verzellesi.
