4 problems

Let $\varphi: Y \to T$ be a flat morphism, let $\mathfrak{a}$ be an $\mathbb{R}$-ideal sheaf on $Y$, and let $\tau: T \to Y$ be a section of $\varphi$. For a closed point $t \in T$…

Let $(X,\mathfrak{a})$ be a log pair, and let $|X|$ denote the set of closed points of $X$ with the Zariski topology. Write $\operatorname{mld}_x(X,\mathfrak{a})$ for the minimal l…

Ignat–Merlet conjecture. Then $(\nabla\varphi_0)^\perp$ is a global minimizer of $\mathcal{I}_f$.

Ambrosio–De Lellis–Mantegazza conjecture. If $f(t)=t^p$ with $1\leq p\leq3$, then $\overline{\mathcal{I}_f}$ is lower semicontinuous for the strong topology in $L^1$.