We prove that, in the first Heisenberg group H, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of H. Moreover two examples are given for stressing result’s sharpness.
The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group / Nicolussi, S.; Serra Cassano, F.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 58:4(2019), pp. 1-28. [10.1007/s00526-019-1581-5]
The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group
Nicolussi S.;Serra Cassano F.
2019-01-01
Abstract
We prove that, in the first Heisenberg group H, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of H. Moreover two examples are given for stressing result’s sharpness.File in questo prodotto:
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