2 problems

Croke–Dairbekov–Sharafutdinov filling-volume conjecture. The filling volume of $\partial X$ with its chordal metric equals $\operatorname{vol}(X)$, and $X$ is the unique volume-min…

Let $K$) be a surface embedded in ${\mathbb{R}}^N$, of genus $g$, and let $\gamma_1,\dots,\gamma_{3g-3}$ be the boundary curves of a pants decomposition of $K$. Here…