Pants decomposition filling-volume conjecture for embedded surfaces

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 $\operatorname{FV}(\gamma_i)$ denotes the filling volume of $\gamma_i$, and $\operatorname{area} K$ denotes the area of $K$. Pants decomposition filling-volume conjecture. There is a pants decomposition such that

$$\sum_i \operatorname{FV}(\gamma_i)\lesssim \operatorname{area} K.$$

The conjecture would give an alternative proof of the proposition that embedded surfaces admit efficient decompositions into simpler integral cycles. The implicit constant is independent of the genus; with genus-dependent constants, the claim follows from the systolic inequality for closed surfaces.