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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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

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

First available in Project Euclid: 7 December 2018

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

isoperimetric surfaces of revolution density


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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