General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux
| dc.creator | Kato, Shin | |
| dc.creator | Umehara, Masaaki | |
| dc.creator | Yamada, Kotaro | |
| dc.date | 1997-09-02 | |
| dc.date.accessioned | 2026-07-07T09:13:19Z | |
| dc.date.available | 2026-07-07T09:13:19Z | |
| dc.description | For each end of complete minimal surface in the Euclidean 3-space, the flux vector is defined. It is well-known that the sum of the flux vector over all ends are zero. Consider the following inverse problem: For each balanced n-vectors, find an n-end catenoid which realizes these vectors as flux. Here, an n-end catenoid is a complete minimal surface of genus zero with ends asymptotic to the catenoids. In this paper, we show that the inverse problem can be solved for almost all balanced n vectors for arbitrary n, which is grater than 4. The assumption "almost all" is needed because nonexistence is known for special balanced vectors. We remark that in the case of n=4, the same result has been obtained by the authors (dg-ga/9709006). And the case n=3 is treated by Lopez and Berbanel. | |
| dc.description | 27 Pages, LaTeX 2.09. See also dg-ga/9709006 | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9709007 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9709007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152285 | |
| dc.subject | Differential Geometry | |
| dc.title | General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux | |
| dc.type | text |