7 problems

Let a simply-connected, bounded Jordan domain be approximated by a sequence of electrical networks, for instance networks arising from a sequence of disk packings. Choose conductan…

A domain in the Riemann sphere $\widehat{\mathbb C}=\mathbb C\cup\{\infty\}$ is a connected open set. A circle domain is a domain whose complementary components are points or close…

Conjectured modulus values.

Let $T_a:\mathbb{B}^2\to\mathbb{B}^2$ be the Möbius transformation … For $x,y,a\in\mathbb{B}^2$ and $\alpha>0$, the generalized point pair function conjecture. … Computer tests sug…

Let $f\colon\mathbb{D}\to\Omega$ be a bounded conformal map from the unit disk, and define the universal integral means spectrum by … where $\beta_f(t)$ is the integral means spect…

The conjectured value of $L(a)$. For $n=2$, numerical experiments suggest that

Let $\Omega\subset \mathbb R^n$ be a bounded open connected domain with $n\geq 3$. Let $u\in W^{1,n}(\Omega)$ and $v\in W^{1,1}(\Omega)$ satisfy … almost everywhere, and suppose th…