Willmore conjecture in codimension 1

Let $g>1$ be an integer, and consider smooth surfaces of $\mathbb{R}^3$ of genus $g$ and their Willmore energy. Willmore conjecture in codimension 1. The only minimizers are the conformal transformations of the Lawson surfaces of genus $g$. The passage states that the complete resolution remains largely open, with recent work addressing surfaces having the same symmetries as the Lawson surfaces.