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A sharp lower bound on the polygonal isoperimetric deficit


Author: Emanuel Indrei
Journal: Proc. Amer. Math. Soc. 144 (2016), 3115-3122
MSC (2010): Primary 52Bxx, 58Cxx; Secondary 51Kxx
DOI: https://doi.org/10.1090/proc/12947
Published electronically: October 22, 2015
MathSciNet review: 3487241
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Emanuel Indrei
Affiliation: Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email: egi@cmu.edu

DOI: https://doi.org/10.1090/proc/12947
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
Article copyright: © Copyright 2015 American Mathematical Society

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