4 problems

An elastic knot is an elastic curve considered in a fixed knot class, with energy minimized among curves in that class. Let the critical composite described in the paper be the tea…

The paper considers the energy … for embedded, arclength-parametrized curves $u:I\to\mathbb{R}^3$, where $\varkappa$ and $\varrho$ are positive and $\operatorname{TP}$ is a tangent…

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 c…

Let ${\mathcal K}$ be a tame knot class, let $\operatorname{bra}{\mathcal K}$ denote its braid index, and let $\operatorname{bri}{\mathcal K}$ denote its bridge index. An $a$-times…