Isoperimetric estimates in products |
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| Authors: | Frank Morgan |
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| Affiliation: | (1) Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA |
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| Abstract: | In a product M 1 × M 2 of Riemannian manifolds, the least perimeter required to enclose given volume among general regions is at least 1/√ 2 times that among regions of product form, assuming that the isoperimetric profiles of M 1 and M 2 are concave. This result sharpens earlier work of Grigor'yan, generalizes results of Bollobás and Leader and of Barthe, and yields a lower bound on the Cheeger isoperimetric constant of a product. |
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| Keywords: | Cheeger constant Isoperimetric profile Product spaces |
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