A proof of the Lawson conjecture for minimal tori embedded in $\S3$
| dc.creator | Pimentel, Fernando A. A. | |
| dc.date | 2007-03-05 | |
| dc.date | 2007-06-18 | |
| dc.date.accessioned | 2026-07-07T08:10:33Z | |
| dc.date.available | 2026-07-07T08:10:33Z | |
| dc.description | A peculiarity of the geometry of the euclidean 3-sphere $\S3$ is that it allows for the existence of compact without boundary minimally immersed surfaces. Despite a wealthy of examples of such surfaces, the only known tori minimally embedded in $\S3$ are the ones congruent to the Clifford torus. In 1970 Lawson conjectured that the Clifford torus is, up to congruences, the only torus minimally embedded in $\S3$. We prove here Lawson conjecture to be true. Two results are instrumental to this work, namely, a characterization of the Clifford torus in terms of its first eingenfunctions (\cite{MR}) and the assumption of a "two-piece property" to these tori: every equator divides a torus minimally embedded in $\S3$ in exactly two connected components (\cite{Rs}). | |
| dc.description | 20 pages, 8 figures, typos corrected (see esp. Lem. 4.2) and clarifications added. We refer esp. to a more straightforward proof of Lemma 3.2, to Rem.3.2, to the statement of Prop. 3.1 and to the definition of the function $Φ_{n,α}^λ$ | |
| dc.identifier | https://arxiv.org/abs/math/0703136 | |
| dc.identifier | http://arxiv.org/abs/math/0703136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131856 | |
| dc.subject | Differential Geometry | |
| dc.title | A proof of the Lawson conjecture for minimal tori embedded in $\S3$ | |
| dc.type | text |