9 problems

Let $\Gamma^0:=\bigcup_{i=1}^nS_i^0$ be an unbounded admissible polygonal curve, and let $\{\Gamma(t)\}_{t\ge0}$ be the globally defined elastic flow with finitely many restarts. W…

Finite-time continuation conjecture. Every finite-time singularity of an unbounded admissible polygonal crystalline elastic flow has the three properties above. The conjecture woul…

Gerriets–Poole's conjecture. A region is a cage if and only if it can accommodate every polygonal worm.

Let the $l$-polygon problem denote the vortex filament evolution whose initial curve is a planar $l$-polygon, and let a one-corner problem denote the corresponding evolution from i…

Fourier-coefficient limit conjecture. Numerical experiments suggest that

Let a regular planar polygon evolve according to the binormal flow. At rational multiples of the time period, consider the resulting curve and the angle between consecutive sides.…

Let $M$ and $q$ be positive integers, let $p$ be coprime with $q$, let $\rho$ be the corner angle, let $\mathbf T_{\mathrm{alg},j}$ be the algebraic tangent vectors of the correspo…

Let $M$ be the number of sides of the initial regular planar polygon, and let $t_{pq}=(2\pi/M^2)(p/q)$, where $p\in\mathbb Z$, $q\in\mathbb N$, and $\gcd(p,q)=1$. At this rational…

DNA inequality conjecture. The DNA inequality holds for arbitrarily small dents of $P$ along side $AB$ if and only if