Open Access
September 2004 Area Inequalities for Embedded Disks Spanning Unknotted Curves
Jeffrey C. Lagarias, Joel Hass, William P. Thurston
J. Differential Geom. 68(1): 1-29 (September 2004). DOI: 10.4310/jdg/1102536708


We show that a smooth unknotted curve in ℝ3 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 → 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.


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Jeffrey C. Lagarias. Joel Hass. William P. Thurston. "Area Inequalities for Embedded Disks Spanning Unknotted Curves." J. Differential Geom. 68 (1) 1 - 29, September 2004.


Published: September 2004
First available in Project Euclid: 8 December 2004

zbMATH: 1104.53006
MathSciNet: MR2152907
Digital Object Identifier: 10.4310/jdg/1102536708

Rights: Copyright © 2004 Lehigh University

Vol.68 • No. 1 • September 2004
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