Summary
Given a symmetric convex bodyC andn hyperplanes in an Euclidean space, there is a translate of a multiple ofC, at least\(\frac{1}{{n + 1}}\) times as large, insideC, whose interior does not meet any of the hyperplanes. The result generalizes Bang's solution of the plank problem of Tarski and has applications to Diophantine approximation.
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Oblatum 25-IX-1990
Partially supported by NSF DMS-8807243
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Ball, K. The plank problem for symmetric bodies. Invent. math. 104, 535–543 (1991). https://doi.org/10.1007/BF01245089
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DOI: https://doi.org/10.1007/BF01245089