Cieliebak–Mohnke's ellipsoid capacity conjecture

Let $0<a_1\le a_2\le\cdots\le a_n<\infty$, and let $E^{2n}(a_1,\dots,a_n)\subset\mathbb{C}^n$ be the ellipsoid defined by

$$E^{2n}(a_1,\dots,a_n)=\left\{(z_1,\dots,z_n)\in\mathbb{C}^n\ \middle|\ \sum_{i=1}^n\frac{\pi|z_i|^2}{a_i}\le1\right\}.$$

For a closed Lagrangian torus $L\subset(X,\omega)$, set

$$A_{\min}(L)=\inf_{\substack{A\in\pi_2(X,L)\\ \int_A\omega>0}}\int_A\omega,$$

and define the Cieliebak–Mohnke capacity by

$$C^{\mathrm{CM}}(X,\omega)=\sup_{\substack{L\subset(X,\omega)\\ L\ \operatorname{Lagrangian\ torus}}}A_{\min}(L).$$

A torus is extremal when $A_{\min}(L)=C^{\mathrm{CM}}(X,\omega)$. Cieliebak–Mohnke's ellipsoid capacity conjecture.

$$C^{\mathrm{CM}}\left(E^{2n}(a_1,\dots,a_n)\right)=\left(\frac1{a_1}+\frac1{a_2}+\cdots+\frac1{a_n}\right)^{-1}.$$

This is attributed in the source to Cieliebak and Mohnke and gives a proposed explicit formula for the Lagrangian capacity of ellipsoids; its resolution is not stated in the supplied text.