Abstract
The classical isoperimetric problem for volumes is solved in ℝ×n(1). Minimizers are shown to be invariant under the group O(n) acting standardly on \({\mathbb{S}}\) n, via a symmetrization argument, and are then classified. Solutions are found among two (one-parameter) families: balls and sections of the form [a, b] ×\({\mathbb{S}}\) n. It is shown that the minimizers may be of both types. For n= 2, it is shown that the transition between the two families occurs exactly once. Some results for general n are also presented.
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Pedrosa, R.H.L. The Isoperimetric Problem in Spherical Cylinders. Annals of Global Analysis and Geometry 26, 333–354 (2004). https://doi.org/10.1023/B:AGAG.0000047528.20962.e2
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DOI: https://doi.org/10.1023/B:AGAG.0000047528.20962.e2