Characterization of ideal knots

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Regularizing and self-avoidance effects of integral Menger curvature (2010, unknown): “However, the thickness [·] depends not only highly nonlinearly but also in a nonsmooth fashion on the curve γ , a fact which turned out to be a challenge for regularity investigations [30, 31, 4], and for numerical treatment [1, 6, 7].”
On rectifiable curves with Lp-bounds on global curvature: self-avoidance, regularity, and minimizing knots (2007, background): “4), turned out to be quite challenging, see [42], [43], [7], [14].”
Integral Menger curvature for surfaces (2009, background): “with positive thickness, are exactly those embeddings with a C1,1-arclength parametrization, which lead to variational applications for nonlinearly elastic curves and rods with positive thickness; see also [30], [31].”
Criticality for the Gehring link problem (2004, methodology): “We note that von der Mosel and Schuricht [ 33 ] have used a similar approach (via Clarke’s theorem and a functional-analytic version of Lagrange multipliers) to derive necessary, but not sufficient, conditions for criticality for the ropelength functional of [4].”
What are the Longest Ropes on the Unit Sphere? (2011, unknown): “see [2,7,21].”
Tangent-point self-avoidance energies for curves (2010, background): “[15], [7], [21]–[23], [12], [13], and has been studied numerically; see e.”