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Isoperimetric regions in \(\mathbb R^{n}\) with density \(r^{p}\). (English) Zbl 1350.49060

Summary: We show that the unique isoperimetric regions in \(\mathbb R^{n}\) with density \(r^{p}\) for \(n\geq 3\) and \(p > 0\) are balls with boundary through the origin.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
52B60 Isoperimetric problems for polytopes
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References:

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