Author:
Cheng Jih-Hsin,Chiu Hung-Lin,Hwang Jenn-Fang,Yang Paul
Abstract
Abstract
For every
{n\geq 2}
we define a notion of umbilicity for hypersurfaces in the Heisenberg group
{H_{n}}
. We classify umbilic hypersurfaces in some cases,
and prove that Pansu spheres are the only umbilic spheres with positive
constant p-mean (or horizontal-mean) curvature in
{H_{n}}
up to Heisenberg
translations.
Funder
National Science Foundation
Subject
Applied Mathematics,General Mathematics
Reference40 articles.
1. Existence and uniqueness for p-area minimizers in the Heisenberg group;Math. Ann.,2007
2. Uniqueness of generalized p-area minimizers and integrability of a horizontal normal in the Heisenberg group;Calc. Var. Partial Differential Equations,2014
3. Minimal surfaces in pseudohermitian geometry;Ann. Sc. Norm. Super. Pisa Cl. Sci. (5),2005
4. Properly embedded and immersed minimal surfaces in the Heisenberg group;Bull. Aust. Math. Soc.,2004
5. A Codazzi-like equation and the singular set for C1{C^{1}} smooth surfaces in the Heisenberg group;J. reine angew. Math.,2012
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献