Slicing convex bodies—bounds for slice area in terms of the body’s covariance
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- by Douglas Hensley PDF
- Proc. Amer. Math. Soc. 79 (1980), 619-625 Request permission
Abstract:
Let Q be a zero-symmetric convex set in ${{\mathbf {R}}^N}$ with volume 1 and covariance matrix $V^2 \mathrm {Id}_{N \times N}$. Let P be a K-dimensional vector subspace of ${{\mathbf {R}}^n},K < N$, and let $J = N - K$. Then there exist constants ${C_1}(J)$ and ${C_2}(J)$ such that \[ {V^{ - J}}{C_1}(J) \leqslant \mathrm {vol}_K(P \cap Q) \leqslant V^{-J}{C_2}(J).\] The lower bound has applications to Diophantine equations.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 619-625
- MSC: Primary 52A40
- DOI: https://doi.org/10.1090/S0002-9939-1980-0572315-5
- MathSciNet review: 572315