@article{61eccd4a5124443390eee17c5e8ec496,
title = "Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group",
abstract = "We study immersed, connected, umbilic hypersurfaces in the Heisenberg group Hn 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.",
keywords = "32V20, 49Q10, 53A10, Primary 35L80, Secondary 35J70",
author = "Cheng, {Jih Hsin} and Chiu, {Hung Lin} and Hwang, {Jenn Fang} and Paul Yang",
note = "Funding Information: J.-H. C. (P. Y., resp.) is grateful to Princeton University (Academia Sinica in Taiwan, resp.) for the kind hospitality. J.-H. C., H.-L. C., and J.-F. H. would like to thank the Ministry of Science and Technology of Taiwan for the support of the following research projects: MOST104-2115-M-001-011-MY2, MOST104-2115-M-008-003-MY2, and MOST104-2115-M-001-009-MY2, resp. P. Y. would like to thank the NSF of the United States for the grant DMS 1509505. H.-L. C. would also like to thank the NCTS of Taiwan for the support. Besides, we would also like to thank Ms. Yu-Tuan Lin and Ms. Li-Yu Huang for the computer assistance to draw figures. Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",
year = "2016",
month = jun,
day = "1",
doi = "10.1007/s00526-016-1006-7",
language = "English (US)",
volume = "55",
journal = "Calculus of Variations and Partial Differential Equations",
issn = "0944-2669",
publisher = "Springer New York",
number = "3",
}