7 problems

Consider the direct-limit coefficient group $\mathbb{Q}/\mathbb{Z}$ obtained from the groups $\mathbb{Z}/n\mathbb{Z}$ under the multiplication maps, equipped with the norm induced…

Let $P$ and $Q$ be a pair of planes, and let the characterizing angles of the pair be defined as in the preceding classification discussion. Morgan's mod-3 conjecture. The pair is…

Let $P$ and $Q$ be oriented planes. Morgan's mod-2 conjecture. The pair $(P,Q)$ is $\mathbb{Z}/2\mathbb{Z}$-area-minimizing if and only if it is $\mathbb{Z}$-area-minimizing with a…

Let $d$ and $c$ be positive integers, and let $T$ be a $d$-dimensional $\mathbb{Z}$-area-minimizing integral current in $\mathbb{R}^{d+c}$. Assume that $T$ has Euclidean volume gro…

Let $M$ be the setting of the preceding discussion, let $d$ be the chain dimension, and let $g$ be a Riemannian metric. For each $n$, consider the proportion in the displayed limin…

Let $T$ be a co-dimension one area-minimizing locally rectifiable current with $C^{1,\alpha}$ tangentially immersed boundary, where $\alpha\in(0,1]$. Let $x$ be a point in the supp…

Let $T$ be an $n$-dimensional area-minimizing locally rectifiable current in $\mathbf{R}^{n+1}$ with $C^{1,\alpha}$ tangentially immersed boundary, where $\alpha\in(0,1)$, and supp…