Koebe's circle-domain conjecture (Kreisnormierungsproblem)

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Lean: release scope note for this family evidence for this event

This event attributed to Unreleased internal OpenAI model

VibeMathed record: Koebe's circle-domain conjecture (Kreisnormierungsproblem) evidence for this event

Koebe (1908), digitized article record evidence for this event

Lean comparator statement: circle-domain theorem and removable-boundary rigidity evidence for this event

Lean: solution module (koebe_circle_domain, removability_implies_rigidity) evidence for this event

Koebe's circle-domain conjecture (Kreisnormierungsproblem) parent of this event

Companion: Koebe's Circle-Domain Conjecture (supplies the transfer theorem used here) evidence for this event

He-Schramm rigidity conjecture: circle domains with conformally removable boundary are rigid evidence for this event

Claims that every domain in $\hat{\mathbb C}$ is conformally equivalent to a circle domain, with no countability or geometric condition on the complementary components. The method marks countably many components, collapses unmarked ones to points with small energy barriers, and shows marked ones become exactly round disks, using transboundary extremal length and a modulus-probability duality. Combined with Ntalampekos-Rajala it also gives a convergent exhaustion by finitely connected domains. It does NOT give uniqueness of the circle-domain model; the rigidity question is the companion's subject and is answered there only under conformal removability of the boundary. parent of this event