Ideal Knots

8 March 2004
Friedemann Schuricht
Let gamma be a closed knotted curve in R^3 such that the tubular neighborhood U_r (gamma) with given radius r>0 does not intersect itself. The length minimizing curve gamma_0 within a prescribed knot class is called ideal knot. We use a special representation of curves and tools from nonsmooth analysis to derive a characterization of ideal knots. Analogous methods can be used for the treatment of self contact of elastic rods.
  • Applied Analysis and Mechanics Seminar