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November 2018 Isoperimetry in Surfaces of Revolution with Density
Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar, Nat Sothanaphan
Missouri J. Math. Sci. 30(2): 150-165 (November 2018). DOI: 10.35834/mjms/1544151692

Abstract

The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-convex density conjecture, for many densities on $\mathbb{R}^n$, the answer is a sphere about the origin. We seek to generalize his results to some other spaces of revolution or to two different densities for volume and perimeter. We provide general results on existence and boundedness and a new approach to proving circles about the origin isoperimetric.

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Eliot Bongiovanni. Alejandro Diaz. Arjun Kakkar. Nat Sothanaphan. "Isoperimetry in Surfaces of Revolution with Density." Missouri J. Math. Sci. 30 (2) 150 - 165, November 2018. https://doi.org/10.35834/mjms/1544151692

Information

Published: November 2018
First available in Project Euclid: 7 December 2018

zbMATH: 07063851
MathSciNet: MR3884737
Digital Object Identifier: 10.35834/mjms/1544151692

Subjects:
Primary: 51F99

Rights: Copyright © 2018 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.30 • No. 2 • November 2018
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