On the Willmore energy of flat $n$-tori in $\mathbb{R}^N$ and Chen's conjecture for $n$-tori

This paper establishes the sharp lower bound $(4nπ^2)^{n/2}$ for the Willmore energy $\mathcal{W}$ of flat $n$-tori in the Euclidean space. Up to Möbius transformations, the Clifford $n$-torus $\mathbb{S}^1\bigl(\sqrt{1/n}\,\bigr) \times \cdots \times \mathbb{S}^1\bigl(\sqrt{1/n}\,\bigr) \subset \ma