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math.DG2024★ 1 cited
Curvature estimates for minimal hypersurfaces in the Heisenberg group
Gianmarco Giovannardi, Andrea Pinamonti, Simone Verzellesi
This paper examines minimal hypersurfaces in sub-Riemannian Heisenberg groups. We extend the celebrated Simons formula and Kato inequality to the sub-Riemannian setting, and we app…
math.DG2024★ 1 cited
Existence and uniqueness of -graphs of prescribed mean curvature in Heisenberg groups
Julián Pozuelo, Simone Verzellesi
We study the prescribed mean curvature equation for -graphs in a Riemannian Heisenberg group of arbitrary dimension. We characterize the existence of classical solutions in a bo…