Regularity of C^{1} smooth surfaces with prescribed p-mean curvature in the Heisenberg group
| dc.creator | Cheng, Jih-Hsin | |
| dc.creator | Hwang, Jenn-Fang | |
| dc.creator | Yang, Paul | |
| dc.date | 2007-09-12 | |
| dc.date | 2008-07-24 | |
| dc.date.accessioned | 2026-07-07T09:52:12Z | |
| dc.date.available | 2026-07-07T09:52:12Z | |
| dc.description | We consider a $C^{1}$ smooth surface with prescribed $p$(or $H$)-mean curvature in the 3-dimensional Heisenberg group. Assuming only the prescribed $p$-mean curvature $H\in C^{0},$ we show that any characteristic curve is $C^{2}$ smooth and its (line) curvature equals $-H$ in the nonsingular domain$.$ By introducing characteristic coordinates and invoking the jump formulas along characteristic curves, we can prove that the Legendrian (or horizontal) normal gains one more derivative. Therefore the seed curves are $C^{2}$ smooth. We also obtain the uniqueness of characteristic and seed curves passing through a common point under some mild conditions, respectively. These results can be applied to more general situations. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0709.1776 | |
| dc.identifier | http://arxiv.org/abs/0709.1776 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165510 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L80; 35J70; 32V20; 53A10; 49Q10 | |
| dc.title | Regularity of C^{1} smooth surfaces with prescribed p-mean curvature in the Heisenberg group | |
| dc.type | text |