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Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group
- Publication Year :
- 2021
-
Abstract
- In this paper, we give a necessary and sufficient condition for a graphical strip in the Heisenberg group $\mathbb{H}$ to be area-minimizing in the slab $\{-1<x<1\}$. We show that our condition is necessary by introducing a family of deformations of graphical strips based on varying a vertical curve. We show that it is sufficient by showing that strips satisfying the condition have monotone epigraphs. We use this condition to show that any area-minimizing ruled entire intrinsic graph in the Heisenberg group is a vertical plane and to find a boundary curve that admits uncountably many fillings by area-minimizing surfaces.<br />Comment: 30 pages, 5 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2105.08890
- Document Type :
- Working Paper