Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group H^n
| dc.creator | Ritoré, Manuel | |
| dc.creator | Rosales, César | |
| dc.date | 2005-04-21 | |
| dc.date.accessioned | 2026-07-07T05:19:19Z | |
| dc.date.available | 2026-07-07T05:19:19Z | |
| dc.description | In this paper we study sets in the $n$-dimensional Heisenberg group $\hhn$ which are critical points, under a volume constraint, of the sub-Riemannian perimeter associated to the distribution of horizontal vector fields in $\hhn$. We define a notion of mean curvature for hypersurfaces and we show that the boundary of a stationary set is a constant mean curvature (CMC) hypersurface. Our definition coincides with previous ones. Our main result describes which are the CMC hypersurfaces of revolution in $\hhn$. The fact that such a hypersurface is invariant under a compact group of rotations allows us to reduce the CMC partial differential equation to a system of ordinary differential equations. The analysis of the solutions leads us to establish a counterpart in the Heisenberg group of the Delaunay classification of constant mean curvature hypersurfaces of revolution in the Euclidean space. Hence we classify the rotationally invariant isoperimetric sets in $\hhn$. | |
| dc.description | 16 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0504439 | |
| dc.identifier | http://arxiv.org/abs/math/0504439 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74977 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | Primary 53C17, Secondary 49Q20 | |
| dc.title | Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group H^n | |
| dc.type | text |