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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.|
|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|
|Pages:||1393 - 1435|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||MATHEMATISCHE ANNALEN|
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