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Strong maximum principle for mean curvature operators on subRiemannian manifolds

Author(s): Cheng, Jih-Hsin; Chiu, Hung-Lin; Hwang, Jenn-Fang; Yang, Paul C.

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dc.contributor.authorCheng, Jih-Hsin-
dc.contributor.authorChiu, Hung-Lin-
dc.contributor.authorHwang, Jenn-Fang-
dc.contributor.authorYang, Paul C.-
dc.identifier.citationCheng, Jih-Hsin, Chiu, Hung-Lin, Hwang, Jenn-Fang, Yang, Paul. (2018). Strong maximum principle for mean curvature operators on subRiemannian manifolds. MATHEMATISCHE ANNALEN, 372 (1393 - 1435). doi:10.1007/s00208-018-1700-1en_US
dc.description.abstractWe study the strong maximum principle for horizontal (p-)mean curvature operator and p-(sub)Laplacian operator on subRiemannian manifolds including, in particular, Heisenberg groups and Heisenberg cylinders. Under a certain Hormander type condition on vector fields, we show the strong maximum principle holds in higher dimensions for two cases: (a) the touching point is nonsingular; (b) the touching point is an isolated singular point for one of comparison functions. For a background subRiemannian manifold with local symmetry of isometric translations, we have the strong maximum principle for associated graphs which include, among others, intrinsic graphs with constant horizontal (p-)mean curvature. As applications, we show a rigidity result of horizontal (p-)minimal hypersurfaces in any higher dimensional Heisenberg cylinder and a pseudo-halfspace theorem for any Heisenberg group.en_US
dc.format.extent1393 - 1435en_US
dc.relation.ispartofMATHEMATISCHE ANNALENen_US
dc.rightsAuthor's manuscripten_US
dc.titleStrong maximum principle for mean curvature operators on subRiemannian manifoldsen_US
dc.typeJournal Articleen_US

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