7 problems

Let the irrigated measure be the measure describing the deviation of the boundary magnetization from the uniform state in the branched transport model associated with the reduced t…

Let $s\in(0,1)$, $d\in\mathbb{N}$, and let $\mu=\mu_t\otimes dt$ be the measure describing the normal phase in the periodic sample $\mathbb{T}^d_T$. For almost every $t$, write … w…

Consider the branched transport energy functional referred to as … , then $\mu_{\pm T}$ is of dimension $8/5$. This conjecture predicts the Hausdorff dimension of the boundary trac…

Let $\beta$ satisfy $0<\beta<1$, and consider the extended dynamic Monge–Kantorovich model with this exponent. Define … Let the CTP denote the comparison transport problem discusse…

Let $\Omega$ be the domain, let $f=f^+-f^-$ be the prescribed source term, and let $(\mu(t),u(t))$ solve the extended dynamic Monge–Kantorovich equations with initial datum $\mu_0$…

Let $A$ be an optimal unit-volume set for irrigation from a single source at the origin in branched transport, and let $\beta=d\left(\alpha-\left(1-1/d\right)\right)\in(0,1)$, wher…

Branching conjecture. For $T<T_*$, every minimizer of $E(T)$ branches at time zero. Equivalently, for sufficiently small $\varepsilon>0$,