TY - JOUR
T1 - Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group
AU - Young, Robert
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/8
Y1 - 2022/8
N2 - In this paper, we give a necessary and sufficient condition for a graphical strip in the Heisenberg group 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.
AB - In this paper, we give a necessary and sufficient condition for a graphical strip in the Heisenberg group 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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U2 - 10.1007/s00526-022-02264-x
DO - 10.1007/s00526-022-02264-x
M3 - Article
AN - SCOPUS:85131071092
SN - 0944-2669
VL - 61
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 4
M1 - 142
ER -