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Estimates for Measures of Sections of Convex Bodies

Part of the Lecture Notes in Mathematics book series (LNM,volume 2116)

Abstract

A \(\sqrt{n}\) estimate in the hyperplane problem with arbitrary measures has recently been proved in [12]. In this note we present analogs of this result for sections of lower dimensions and in the complex case. We deduce these inequalities from stability in comparison problems for different generalizations of intersection bodies.

Keywords

  • Convex Body
  • Intersection Body
  • Continuous Density
  • Star Body
  • Arbitrary Measure

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Acknowledgements

I wish to thank the US National Science Foundation for support through grant DMS-1265155.

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Correspondence to Alexander Koldobsky .

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Koldobsky, A. (2014). Estimates for Measures of Sections of Convex Bodies. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_17

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