Oh's conjecture on Hamiltonian volume minimization of product tori

Let $T(\boldsymbol{b})=T(b_1,\ldots,b_n)=S^1(b_1)\times\cdots\times S^1(b_n)\subset\mathbb C^n$ be the product Lagrangian torus, where each $b_i>0$ and $S^1(b_i)$ is the circle bounding a disc of area $b_i$.

Oh's conjecture. The Lagrangian torus $T(\boldsymbol{b})$ in $\mathbb C^n$ is Hamiltonian volume minimizing.

The claim would extend the one-dimensional isoperimetric inequality to product Lagrangian tori. The source presents it as a conjecture based on the Hamiltonian minimality and Hamiltonian stability of these tori, but the supplied text gives no resolution status.