## Volume difference inequalities

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- by Apostolos Giannopoulos and Alexander Koldobsky PDF
- Trans. Amer. Math. Soc.
**370**(2018), 4351-4372 Request permission

## Abstract:

We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is replaced by an arbitrary measure.## References

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## Additional Information

**Apostolos Giannopoulos**- Affiliation: Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis 157-84, Athens, Greece
- Email: apgiannop@math.uoa.gr
**Alexander Koldobsky**- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 104225
- Email: koldobskiya@missouri.edu
- Received by editor(s): August 11, 2016
- Received by editor(s) in revised form: December 17, 2016
- Published electronically: February 19, 2018
- Additional Notes: The second named author was supported in part by the NSF grant DMS-1265155
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**370**(2018), 4351-4372 - MSC (2010): Primary 52A20; Secondary 46B06
- DOI: https://doi.org/10.1090/tran/7173
- MathSciNet review: 3811531