An inverse problem of the flux for minimal surfaces
| 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 a complete minimal surface in the Euclidean 3-space, the so-called flux vector corresponds to each end. The flux vectors are balanced, i.e., the sum of those over all ends are zero. Consider the following inverse problem: For each balanced n vectors, find an n-end catenoid which attains given vectors as flux. Here, an n-end catenoid is a complete minimal surface of genus 0 with ends asymptotic to the catenoids. In this paper, the problem is reduced to solving algebraic equation. Using this reduction, it is shown that, when n=4, the inverse problem for 4-end catenoid has solutions for almost all balanced 4 vectors. Further obstructions for n-end catenoids with parallel flux vectors are also discussed. | |
| dc.description | 28 pages, AMSLaTeX 1.1, with 8 figures, To appear in Indiana University Mathematics Journal | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9709006 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9709006 | |
| dc.identifier | Indiana Univ. Math. J., vol. 46 (1997) 529--560 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152284 | |
| dc.subject | Differential Geometry | |
| dc.title | An inverse problem of the flux for minimal surfaces | |
| dc.type | text |