Covering space with translates of convex shapes.
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For every convex body K in R^n, n≥1, the manuscript reports volume product at its Santaló point at least (n+1)^(n+1)/(n!)², with equality exactly for simplices.
Original report: 2026-10-06The manuscript reports density at most C n log n for a single-lattice covering by translates of every convex body in dimension n ≥ 2.
Read original source Original manuscript · family 092github.com
Original report: 2026-10-06Covering space with translates of convex shapes. Density, dimension, and the permitted translation pattern determine which bounds can be compared.
This topic groups related mathematical questions across publishers. Each focused problem carries its own baseline and each contribution retains its original source. Results are compared only when their assumptions, optimization target, and computation model agree.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
OpenAI reports: Mahler’s conjecture for general convex bodies
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