TY - JOUR
T1 - Strong maximum principle for mean curvature operators on subRiemannian manifolds
AU - Cheng, Jih Hsin
AU - Chiu, Hung Lin
AU - Hwang, Jenn Fang
AU - Yang, Paul
N1 - Funding Information:
Acknowledgements J.-H. Cheng, H.-L. Chiu, and J.-F. Hwang would like to thank the Ministry of Science and Technology of Taiwan for the support of the projects: MOST 104-2115-M-001-011-MY2, 104-2115-M-008-003-MY2, and 104-2115-M-001-009-MY2, resp. J.-H. Cheng is also grateful to the National Center for Theoretical Sciences of Taiwan for the constant support. P. Yang would like to thank the NSF of the US for the support of the project: DMS-1509505.
Funding Information:
J.-H. Cheng, H.-L. Chiu, and J.-F. Hwang would like to thank the Ministry of Science and Technology of Taiwan for the support of the projects: MOST 104-2115-M-001-011-MY2, 104-2115-M-008-003-MY2, and 104-2115-M-001-009-MY2, resp. J.-H. Cheng is also grateful to the National Center for Theoretical Sciences of Taiwan for the constant support. P. Yang would like to thank the NSF of the US for the support of the project: DMS-1509505.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00208-018-1700-1
DO - 10.1007/s00208-018-1700-1
M3 - Article
AN - SCOPUS:85047942297
VL - 372
SP - 1393
EP - 1435
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 3-4
ER -