5 problems

Let $\Gamma$ be a prism of a hexagonal tessellation of the Klein bottle, and suppose its cutout contains an $m\times n$ array of tiles, with $m$ and $n$ even. Assume that both type…

Jakobson–Nadirashvili–Polterovich conjecture. The value $p=\sqrt{3/8}$ is the only value in $(0,1]$ that corresponds to a periodic solution satisfying these conditions. The value…

Uniqueness conjecture for the periodic solution. The value $p=\sqrt{3/8}$ is the only value corresponding to a periodic solution satisfying these conditions.

Uniqueness conjecture for the maximizing metric. The value $12\pi E(2\sqrt{2}/3)$ is uniquely achieved, up to a dilatation, by $g_0$.

Let $\mathbb{KL}$ be the Klein bottle, and let $\tilde{\tau}_{3,1}$ denote the bipolar Lawson surface equipped with its induced metric. For a Riemannian metric $g$ on $\mathbb{KL}$…