Uniqueness conjecture for minimal embeddings of the three-dimensional torus in the four-sphere

Let $T^3=S^1\times S^1\times S^1$ be the three-dimensional torus, embedded minimally in the round four-dimensional sphere $\mathbb{S}^4$. Two embeddings are considered equivalent if they differ by an ambient isometry. Uniqueness conjecture for the Clifford torus. There exists, up to ambient isometry, a unique minimal embedding of $T^3$ in $\mathbb{S}^4$. Numerical simulations suggest uniqueness of the corresponding closed periodic orbit and motivate this stronger claim in the case $n=2$. These questions are described as challenging open problems.