%0 Journal Article
%T Area Inequalities for Embedded Disks Spanning Unknotted Curves
%A Joel Hass
%A Jeffrey C. Lagarias
%A William P. Thurston
%J Mathematics
%D 2003
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0306313v2