## 摘要

In the first Heisenberg group ℍ^{1} with its sub-Riemannian struc-ture generated by the horizontal subbundle, we single out a class of C^{2} non-characteristic entire intrinsic graphs which we call strict graphical strips. We prove that such strict graphical strips have vanishing horizontal mean curvature (i.e., they are H-minimal) and are unstable (i.e., there exist compactly supported deforma-tions for which the second variation of the horizontal perimeter is strictly negative). We then show that, modulo left-translations and rotations about the center of the group, every C^{2} entire H-minimal graph with empty characteristic locus and which is not a vertical plane contains a strict graphical strip. Combining these results we prove the conjecture that in ℍ^{1} the only stable C2 H- minimal entire graphs, with empty characteristic locus, are the vertical planes.

原文 | ???core.languages.en_GB??? |
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頁（從 - 到） | 251-295 |

頁數 | 45 |

期刊 | Journal of Differential Geometry |

卷 | 81 |

發行號 | 2 |

DOIs | |

出版狀態 | 已出版 - 2009 |

## 指紋

深入研究「Instability of graphical strips and a positive answer to the bernstein problem in the heisenberg group ℍ^{1}」主題。共同形成了獨特的指紋。