Compact minimal vertical graphs with non-connected boundary in ℍⁿ×ℝ

2013/03/13 by Barbosa, Aline Mauricio
#35J25 #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1303.3089

Abstract

We study the existence and uniqueness problem of compact minimal vertical graphs in ℍⁿ×ℝ, n≥ 2, over bounded domains in the slice ℍⁿ×\0\, with non-connected boundary having a finite number of C⁰ hypersufaces homeomorphic to the sphere \mathbbS^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 ℍⁿ×ℝ having the boundary in two slices and the height greater than or equal to π/(2n-2).

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