4 problems

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Freedman–He conjecture on the conformal capacity of solid tori
Freedman–He conjecture. For every solid torus $T\subset\mathbb S^3$ ,
Conjectureopenconformal-capacity conformal-geometry solid-toriarXiv posted 2 days ago
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Gehring–Martin–Palka conjecture on the conformal capacity of linked curves
Gehring–Martin–Palka conjecture. Every pair of linked curves satisfies
Conjectureopenconformal-capacity conformal-geometry linked-curvesarXiv posted 2 days ago
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The conjectured boundary formula for conformal capacity in dimensions at least three
Boundary formula conjecture. This formula should remain valid for $n\geq 3$ :
Conjectureopenconformal-capacity potential-theoryarXiv posted 2 days ago
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The conjectured Pólya–Szegő inequality for convex bodies in higher dimensions
Higher-dimensional Pólya–Szegő conjecture. The same inequality should hold for every $n\geq 3$ and every convex $K$ :
Conjectureopenconformal-capacity convex-geometry inequalitiesarXiv posted 2 days ago

Freedman–He conjecture on the conformal capacity of solid tori