4 problems

Let $L$ be a link, let $R^p(L)$ be the scale-invariant energy defined in the paper, and let $R(L)$ denote ropelength, with thickness measuring the radius of the largest embedded tu…

Let $L$ be a link, and for $p\geq 1$ let $R^p(L)$ denote the scale-invariant $L^p$ energy defined by integrating inverse powers of the radius function $r(T_xL,y)$. An energy is bas…

Let $e_j^p$ be O'Hara's knot energy, defined for smooth embedded unit-speed curves by … where … and $d(s,t)$ is the shortest distance between $c(s)$ and $c(t)$ along the curve. O'H…

Let $\mathcal{E}^\alpha$ denote O'Hara's knot energy for $2<\alpha<3$. The preceding smoothness result states that finite-energy critical points are smooth, and analyticity is know…