Compact minimal vertical graphs with non-connected boundary in H^n x R
Aline Mauricio Barbosa · arXiv (Cornell University) · 2013
We study the existence and uniqueness problem of compact minimal vertical graphs in H^n x R, n greater than or equal to 2, over bounded domains in the slice H^n x {0}, with non-connected boundary having a finite number of C^0 hypersufaces homeomorphic to the sphere S^{n-1}, with prescribed bounded continuous boundary data, under hypotheses relating those data and the geometry of the boundary. We show the nonexistence of compact minimal vertical graphs in H^n x R having the boundary in two slices and the height greater than or equal to \pi/(2n-2).