Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

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

doi:10.1007/s00526-016-1006-7

Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

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

Mathematics

Research output: Contribution to journal › Article

1 Scopus citations

Abstract

We study immersed, connected, umbilic hypersurfaces in the Heisenberg group H_n with n≥ 2. We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.

Original language	English (US)
Article number	66
Journal	Calculus of Variations and Partial Differential Equations
Volume	55
Issue number	3
DOIs	https://doi.org/10.1007/s00526-016-1006-7
State	Published - Jun 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

32V20
49Q10
53A10
Primary 35L80
Secondary 35J70

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10.1007/s00526-016-1006-7

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Cheng, J. H., Chiu, H. L., Hwang, J. F., & Yang, P. (2016). Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group. Calculus of Variations and Partial Differential Equations, 55(3), [66]. https://doi.org/10.1007/s00526-016-1006-7

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