Calculus of Variations and Geometric Measure Theory

J. Pozuelo - S. Verzellesi

Existence and uniqueness of t-graphs of prescribed mean curvature in Heisenberg groups

created by verzellesi on 10 May 2024



Inserted: 10 may 2024
Last Updated: 10 may 2024

Year: 2024


We study the prescribed mean curvature equation for t-graphs in a Riemannian Heisenberg group of arbitrary dimension. We characterize the existence of classical solutions in a bounded domain without imposing Dirichlet boundary data, and we provide conditions that guarantee uniqueness. Moreover, we extend previous results to solve the Dirichlet problem when the mean curvature is non-constant. Finally, by an approximation technique, we obtain solutions to the sub-Riemannian prescribed mean curvature equation.