geometry-topology / Convex geometry
Dyn and Farkhi conjectured that the squared Hausdorff distance from a compact set to its convex hull is subadditive under Minkowski addition. It holds in dimensions one and two and fails from dimension three; the sharp threshold exponent for Hausdorff convexification is now determined.
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Append-only history
pins the sharp threshold; the conjecture itself was already known false above dimension two
Research memory
Dyn and Farkhi conjectured that the squared Hausdorff distance from a compact set to its convex hull is subadditive under Minkowski addition. It holds in dimensions one and two and fails from dimension three; the sharp threshold exponent for Hausdorff convexification is now determined.
pins the sharp threshold; the conjecture itself was already known false above dimension two
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