4 problems

Let $\Omega\subset\mathbb{C}$ be an extremal domain for analytic content, meaning that it is a bounded domain with real analytic boundary and … An annulus is a domain conformally e…

Let $K\subset\mathbb{C}$ be compact, let $R(K)$ be the uniform closure on $K$ of rational functions with poles outside $K$, and define its analytic content by … For a bounded domai…

Let $\Omega\subset\mathbb{R}^{N}$ be a smoothly bounded domain, let $B=B(1)$ be the unit ball, and let $r_{\Omega}>0$ satisfy $m(B(r_{\Omega}))=m(\Omega)$. For $p\in[1,\infty)$, wr…

Analytic-content extremal-domain conjecture.