Spherical or planar shape conjecture for elastic prime knots

An elastic knot is a knot representative minimizing the bending energy within its knot class, and a prime knot is a knot that cannot be expressed as a nontrivial connected sum. A curve is spherical if it lies on a sphere, and planar if it lies in a plane. Spherical or planar shape conjecture. Any elastic prime knot is a spherical or planar curve. The source describes this as a conjecture communicated by Urs Lang in 1997; the shape of elastic knots in more general knot classes is an ongoing research topic, and no resolution is given.