Area Inequalities for Embedded Disks Spanning Unknotted Curves
| dc.creator | Hass, Joel | |
| dc.creator | Lagarias, Jeffrey C. | |
| dc.creator | Thurston, William P. | |
| dc.date | 2003-06-21 | |
| dc.date | 2004-07-10 | |
| dc.date.accessioned | 2026-07-07T06:23:25Z | |
| dc.date.available | 2026-07-07T06:23:25Z | |
| dc.description | We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the length L of the curve and the thickness r (maximal radius of an embedded tubular neighborhood) of the curve. For fixed length, the expression giving the upper bound on the area grows exponentially in 1/r^2. In the direction of lower bounds, we give a sequence of length one curves with r approaching 0 for which the area of any spanning disk is bounded from below by a function that grows exponentially with 1/r. In particular, given any constant A, there is a smooth, unknotted length one curve for which the area of a smallest embedded spanning disk is greater than A. | |
| dc.description | 31 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0306313 | |
| dc.identifier | http://arxiv.org/abs/math/0306313 | |
| dc.identifier | Journal of Differential Geometry 68, (2004) 1-30. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96222 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | Primary 53A10, Secondary: 52B60, 57Q15 | |
| dc.title | Area Inequalities for Embedded Disks Spanning Unknotted Curves | |
| dc.type | text |