5 problems

Let $\Omega$ be an $n$-connected domain. For each $z\in\Omega$ and each $1\leq k\leq n$, let $\varphi_{z,k}$ be a canonical mapping associated with the boundary component indexed b…

Let $n\ge 4$ equal-strength cavities be represented by a conformal map $\omega$ from a slit domain to the exterior elastic domain $D^e$. Let $\Psi(z)$ be the Kolosov–Muskhelishvili…

Let $D$ be a domain and let $z,w$ be distinct boundary or interior marked points for which the SLE measure $4mu_D(z,w)$ is defined. Write … for its total mass. SLE partition-functi…

Thin-affine nonexistence conjecture. If $\epsilon>0$ is sufficiently small, depending on both $\Omega$ and $\Omega^*$, then there is no energy-minimal homeomorphism of $\Omega$ ont…

Let $\Omega$ and $\Omega^*$ be bounded $k$-connected domains in $\mathbb{C}$, where $k\geqslant 2$. Suppose that $\Omega\subset\Omega^*$ and that the inclusion is a homotopy equiva…