A sharp lower bound on the polygonal isoperimetric deficit
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- by Emanuel Indrei
- Proc. Amer. Math. Soc. 144 (2016), 3115-3122
- DOI: https://doi.org/10.1090/proc/12947
- Published electronically: October 22, 2015
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Abstract:
It is shown that the isoperimetric deficit of a convex polygon $P$ admits a lower bound in terms of the variance of the radii of $P$, the area of $P$, and the variance of the barycentric angles of $P$. The proof involves circulant matrix theory and a Taylor expansion of the deficit on a compact manifold.References
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Bibliographic Information
- Emanuel Indrei
- Affiliation: Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
- MR Author ID: 1009717
- Email: egi@cmu.edu
- Received by editor(s): February 20, 2015
- Received by editor(s) in revised form: August 28, 2015
- Published electronically: October 22, 2015
- Additional Notes: The author is a PIRE Postdoctoral Fellow
- Communicated by: Jeremy Tyson
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3115-3122
- MSC (2010): Primary 52Bxx, 58Cxx; Secondary 51Kxx
- DOI: https://doi.org/10.1090/proc/12947
- MathSciNet review: 3487241