Cube slicing in $\textbf {R}^ n$
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- by Keith Ball
- Proc. Amer. Math. Soc. 97 (1986), 465-473
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840631-0
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Abstract:
We prove that every $(n - 1)$-dimensional section of the unit cube in ${{\mathbf {R}}^n}$ has volume at most $\sqrt 2$. This upper bound is clearly best possible.References
- K. M. Ball, Sections of convex sets in ${{\mathbf {R}}^n}$ (in preparation).
- Uffe Haagerup, The best constants in the Khintchine inequality, Studia Math. 70 (1981), no. 3, 231–283 (1982). MR 654838, DOI 10.4064/sm-70-3-231-283
- Douglas Hensley, Slicing the cube in $\textbf {R}^{n}$ and probability (bounds for the measure of a central cube slice in $\textbf {R}^{n}$ by probability methods), Proc. Amer. Math. Soc. 73 (1979), no. 1, 95–100. MR 512066, DOI 10.1090/S0002-9939-1979-0512066-8
- Jeffrey D. Vaaler, A geometric inequality with applications to linear forms, Pacific J. Math. 83 (1979), no. 2, 543–553. MR 557952, DOI 10.2140/pjm.1979.83.543
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 465-473
- MSC: Primary 60E15; Secondary 52A22, 52A40, 60D05
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840631-0
- MathSciNet review: 840631