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.
|Original language||English (US)|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Jun 1 2016|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Primary 35L80
- Secondary 35J70