Missouri Journal of Mathematical Sciences

Isoperimetry in Surfaces of Revolution with Density

Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar, and Nat Sothanaphan

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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.

Article information

Source
Missouri J. Math. Sci., Volume 30, Issue 2 (2018), 150-165.

Dates
First available in Project Euclid: 7 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1544151692

Digital Object Identifier
doi:10.35834/mjms/1544151692

Mathematical Reviews number (MathSciNet)
MR3884737

Zentralblatt MATH identifier
07063851

Subjects
Primary: 51F99: None of the above, but in this section

Keywords
isoperimetric surfaces of revolution density

Citation

Bongiovanni, Eliot; Diaz, Alejandro; Kakkar, Arjun; Sothanaphan, Nat. Isoperimetry in Surfaces of Revolution with Density. Missouri J. Math. Sci. 30 (2018), no. 2, 150--165. doi:10.35834/mjms/1544151692. https://projecteuclid.org/euclid.mjms/1544151692


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References

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