3 problems

For every integer $n\geq 2$, every integer $N\geq n+1$, and every immersion $f:T^n\to\mathbb{R}^N$ whose induced metric is flat, the Willmore energy…

Let $M^{2}\subset\mathbb{S}^{3}(1)$ be an embedded closed surface of genus one, and suppose that the curvature endomorphism satisfies $\Re|_{\slashed{E}}=0$. Let $\bar{\Gamma}_{1}$…

Let $\mathcal{A}_\gamma$ be the minimum area among all minimal surfaces in $\mathbb{S}^3$ of genus $\gamma$, and let $\xi_{\gamma,1}$ be the Lawson surface of genus $\gamma$. Lawso…