3 problems

A Hopf link is a link consisting of two disjoint circles linked once. Its cross-energy is the interaction energy between the two components, and let its minimum be taken over all g…

Let $cmathscr{M}_p$ denote the integral Menger curvature functional considered in the source, and let the circle be viewed as a knot. Circle-minimizer conjecture. The circle is the…

Let a knot be prime if it cannot be divided into simpler knots, and consider the Möbius energy of a knot. Kusner–Sullivan conjecture. There are no minimizers among non-prime knots.…