We study the isoperimetric problem, the least-perimeter way to enclose given area, in various surfaces. For example, in two-dimensional Twisted Chimney space, a two-dimensional analog of one of the ten flat, orientable models for the universe, we prove that isoperimetric regions are round discs or strips. In the Gauss plane, defined as the Euclidean plane with Gaussian density, we prove that in halfspaces y ≥ a vertical rays minimize perimeter. In Rn with radial density and in certain products we provide partial results and conjectures.
"Isoperimetric Regions in Spaces,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 7:
2, Article 15.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss2/15