An asymmetric convex body with maximal sections of constant volume
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- by Fedor Nazarov, Dmitry Ryabogin and Artem Zvavitch;
- J. Amer. Math. Soc. 27 (2014), 43-68
- DOI: https://doi.org/10.1090/S0894-0347-2013-00777-8
- Published electronically: July 18, 2013
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Abstract:
We show that in all dimensions $d\ge 3$, there exists an asymmetric convex body of revolution all of whose maximal hyperplane sections have the same volume. This gives the negative answer to the question posed by V. Klee in 1969.References
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Bibliographic Information
- Fedor Nazarov
- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
- MR Author ID: 233855
- Email: nazarov@math.kent.edu
- Dmitry Ryabogin
- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
- Email: ryabogin@math.kent.edu
- Artem Zvavitch
- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
- MR Author ID: 671170
- Email: zvavitch@math.kent.edu
- Received by editor(s): January 6, 2012
- Received by editor(s) in revised form: October 4, 2012, and May 31, 2013
- Published electronically: July 18, 2013
- Additional Notes: The first author is supported in part by U.S. National Science Foundation Grant DMS-0800243
The second and third authors are supported in part by U.S. National Science Foundation Grant DMS-1101636. - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 27 (2014), 43-68
- MSC (2010): Primary 52A20, 52A40; Secondary 52A38
- DOI: https://doi.org/10.1090/S0894-0347-2013-00777-8
- MathSciNet review: 3110795