Abstract
We study the geometry of the Heisenberg group with a balanced metric, the sum of the left and right invariant metrics. We prove that with this metric, splits as a Riemannian product , where is a totally geodesic surface and the center of . So we prove the existence of complete properly embedded minimal surfaces in by solving the asymptotic Dirichlet problem for the minimal surface equation on . We also show the existence of complete properly embedded minimal surfaces foliating an open set of having as boundary a given curve Γ in , satisfying the exterior circle condition, by solving the exterior Dirichlet problem for the minimal surface equation in the unbounded connected component of .
Citation
Fidelis Bittencourt. Edson S. Figueiredo. Pedro Fusieger. Jaime Ripoll. "On the geometry of the Heisenberg group with a balanced metric." Illinois J. Math. 67 (1) 33 - 44, April 2023. https://doi.org/10.1215/00192082-10407050
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