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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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Abstract: We 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.
Publication Date: Dec-2018
Electronic Publication Date: 1-Jun-2018
Citation: Cheng, 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/s00208-018-1700-1
DOI: doi:10.1007/s00208-018-1700-1
ISSN: 0025-5831
EISSN: 1432-1807
Pages: 1393 - 1435
Language: English
Type of Material: Journal Article
Journal/Proceeding Title: MATHEMATISCHE ANNALEN
Version: Author's manuscript

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