3 problems

Let $\Omega$ and $\Omega^*$ be bounded doubly connected domains in $\mathbb{C}$, and suppose that there is an energy-minimal diffeomorphism … Write $\operatorname{Mod}\Omega$ and…

Let $\Omega^*$ be a bounded doubly connected domain in $\mathbb{C}$, and let $\mathsf{E}(\tau,\Omega^*)$ denote the infimum of the Dirichlet energy over deformations from a doubly…

Let $\Omega\subset\mathbb C$ be a doubly connected domain, and let $\mathbb C_\circ=\mathbb C\setminus\{0\}$. Suppose $h\colon\Omega\to\mathbb C_\circ$ is harmonic and is not homot…