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تسجيل مستخدم جديدArea-minimizing ruled graphs and the Bernstein problem in the Heisenberg group
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تأليف
Robert Young
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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.
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