5 problems

Let $d$ be the distance function in the setting of Theorem, and let a singularity be a singular point of $d$ from which singularity propagation is considered. The preceding torus e…

For finite sets $A$ and $B$, define, for $p>0$, the quantity … It specializes to $J_1$ when $p=1$ and tends to $J_{\infty}$ as $p\to\infty$. Metricity conjecture. $J_p$ is a metric…

Magnanini's conjecture. The number of critical points satisfies

Let $\Omega\in\mathcal{O}$ be a general domain, let $d$ denote the distance to $\partial\Omega$, and let $v_\tau$ be the minimizing vector fields associated with the drift optimiza…

Let $X$ be a convex surface in ${\mathbb R}^{n+1}$, let $x_0\in X$ be fixed, and consider the distance function $x\mapsto {\rm dist}(x,x_0)$. For $n=1$, this function is DC on all…