Properly embedded and immersed minimal surfaces in the Heisenberg group
| dc.creator | Cheng, Jih-Hsin | |
| dc.creator | Hwang, Jenn-Fang | |
| dc.date | 2004-07-07 | |
| dc.date.accessioned | 2026-07-07T09:32:04Z | |
| dc.date.available | 2026-07-07T09:32:04Z | |
| dc.description | We study properly embedded and immersed p(pseudohermitian)-minimal surfaces in the 3-dimensional Heisenberg group. From the recent work of Cheng, Hwang, Malchiodi, and Yang, we learn that such surfaces must be ruled surfaces. There are two types of such surfaces: band type and annulus type according to their topology. We give an explicit expression for these surfaces. Among band types there is a class of properly embedded p-minimal surfaces of so called helicoid type. We classify all the helicoid type p-minimal surfaces. This class of p-minimal surfaces includes all the entire p-minimal graphs (except contact planes) over any plane. Moreover, we give a necessary and sufficient condition for such a p-minimal surface to have no singular points. For general complete immersed p-minimal surfaces, we prove a half space theorem and give a criterion for the properness. | |
| dc.description | 13 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0407094 | |
| dc.identifier | http://arxiv.org/abs/math/0407094 | |
| dc.identifier | Bull. Aus. Math. Soc., 70 (2004) 507-520. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158679 | |
| dc.subject | Differential Geometry | |
| dc.subject | 35L80; 35J70; 32V20; 53A10; 49Q10 | |
| dc.title | Properly embedded and immersed minimal surfaces in the Heisenberg group | |
| dc.type | text |