On the Isoperimetric Constants for Product Measures
نویسندگان
چکیده
This quantity was introduced in 1969 by Cheeger [1] to bound from below the spectral gap of the Laplacian on compact Riemannian manifolds, and nowadays (1) is often called an isoperimetric inequality of the Cheeger type. The relationship between more general isoperimetric and certain Sobolev type inequalities was earlier considered by Maz’ya [2] (see for history, for example, [3, 4]). What was noticed in [1] as an equivalent functional form for (1) (in the framework of Riemannian manifolds) is that, for any smooth function f on M with μ-median m, we have
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