3 problems

Let $(\mathsf{X},\mathsf{d},\mathfrak{m})$ be a $PI$ space, let $\Omega\subset\mathsf{X}$ be open, and let $u\in\mathsf{BV}(\Omega)$. Define the area of $u$ in a measurable set…

Semmes' weak-tangent conjecture. There is a weak tangent of $f$ that is bi-Lipschitz. This is a formulation of the positive-rigidity questions for Lipschitz maps from PI spaces int…

Semmes' conjecture. There is a subset $E\subset A$ such that $\mathcal{H}^Q(E)>0$ and $f$ is bi-Lipschitz on $E$. This conjecture concerns when a Lipschitz map from a PI space into…