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

## Author(s): Cheng, Jih-Hsin; Chiu, Hung-Lin; Hwang, Jenn-Fang; Yang, Paul C.

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 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. Publication Date: Jun-2016 Electronic Publication Date: 24-May-2016 Citation: Cheng, Jih-Hsin, Chiu, Hung-Lin, Hwang, Jenn-Fang, Yang, Paul. (2016). Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 55, doi:10.1007/s00526-016-1006-7 DOI: doi:10.1007/s00526-016-1006-7 ISSN: 0944-2669 EISSN: 1432-0835 Pages: 1 - 28 Language: English Type of Material: Journal Article Journal/Proceeding Title: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Version: Author's manuscript