Strong maximum principle for mean curvature operators on subRiemannian manifolds

Jih Hsin Cheng, Hung Lin Chiu, Jenn Fang Hwang, Paul Yang

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1393-1435
Number of pages43
JournalMathematische Annalen
Volume372
Issue number3-4
DOIs
StatePublished - Dec 1 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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