EXISTENCE OF IDEAL KNOTS

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What are the Longest Ropes on the Unit Sphere? (2011, background): “Related variational problems in the context of nonlinearly elastic curves and rods with the same notion of thickness, in particular the existence of ideal knots, were treated in [13]; for ideal knots and links see also [3,11].”
Regularizing and self-avoidance effects of integral Menger curvature (2010, unknown): “This result was the starting point for a number of variational applications involving curves or elastic rods with positive thickness and under topological constraints [15, 5, 13, 11, 12].”
Characterization of ideal knots (2004, methodology): “Meanwhile the existence of ideal knots for each knot type was shown independently in [3,7, 8 ].”
On rectifiable curves with Lp-bounds on global curvature: self-avoidance, regularity, and minimizing knots (2007, background): “In that context the global radius of curvature introduced by Gonzalez and Maddocks [20] turned out to be both a mathematically precise and analytically tractable notion to tackle energy minimization problems in nonlinear elasticity and knot theory for curves and rods with a given thickness [22], [8]”