3 problems

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Jones's conjecture on the function-theoretic extremality of $(\epsilon,\delta)$ domains
Let $\Omega\subset\mathbb R^n$ be an $(\epsilon,\delta)$ domain, meaning a domain satisfying the quantitative curve-connectivity condition introduced by Jones. Such domains are Jon…
Conjecturesolvedextension-domains function-theory uniform-domainsarXiv posted 2 days ago
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Minimizer conjecture for weighted fillings in Sobolev extension domains
Weighted filling minimizer conjecture. This minimization problem should provide the relevant generalization for weighted fillings of codimension-one spheres in $O$ ; in particular,…
Conjectureopenextension-domains geometric-measure-theory sobolev-spacesarXiv posted 2 days ago
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Koski–Mäkinen–? quasiconvexity conjecture for complements of Sobolev extension domains
Quasiconvexity conjecture. The complement of every $W^{1,p}$ -extension domain with $1<p\le2$ is quasiconvex.
Conjectureopenextension-domains quasiconvexity sobolev-spacesarXiv posted 2 days ago

Jones's conjecture on the function-theoretic extremality of (ϵ,δ)(\epsilon,\delta)(ϵ,δ) domains