Bang's half-area cylinder covering question (and the 1-codimensional cylinder covering conjecture)

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Lean formalization: CylinderCovering/Main.lean (four-paper aggregate) evidence for this event

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Bang's half-area cylinder covering question (and the 1-codimensional cylinder covering conjecture) parent of this event

Theorem 1.1: a regular tetrahedron $K$ with $A_{\min}(K)=\sqrt2$ has, for each $0<\varepsilon\le1/2000$, a cover by $2\lceil2/\varepsilon^2\rceil$ cylinders with compact triangular perpendicular bases and $\frac1{\sqrt2}\sum|B_i|=\frac12-\frac{13}{6000}\varepsilon^2+O(\varepsilon^4)$, strictly below half. Corollary 1.2: every nondegenerate tetrahedron has a finite cover with directionwise relative cost below 1/2, refuting the Bezdek-Khan conjecture. Not shown: the optimal constant (Bezdek-Litvak's lower bound 1/3 stands) or counterexamples among centrally symmetric bodies. parent of this event

Bezdek-Khan, The geometry of homothetic covering and illumination (Conjecture 4.13) evidence for this event

Companion: Finite cylinder approximation of ruled sets evidence for this event

VibeMathed record: Bang's half-area cylinder covering question (and the 1-codimensional cylinder covering conjecture) evidence for this event

Companion: Slope-field perturbations of the two-cylinder covering evidence for this event

Lean formalization: TriangularCovering/Main.lean evidence for this event

Companion: Finite triangular approximation of radial sweeps evidence for this event

Bang's half-area cylinder covering question (and the 1-codimensional cylinder covering conjecture) evidence for this event