A Faber-krahn Inequality for the Cheeger Constant of N-gons
نویسندگان
چکیده
We prove that the regular N -gon minimizes the Cheeger constant among polygons with a given area and N sides.
منابع مشابه
A Note on Cheeger Sets
Starting from the quantitative isoperimetric inequality [21, 17], we prove a sharp quantitative version of the Cheeger inequality. A Cheeger set E for an open subset Ω ⊂ R, n ≥ 2, is any minimizer of the variational problem cm(Ω) = inf { P (E) |E|m : E ⊂ Ω , 0 < |E| < ∞ } , (1) where |E| is the Lebesgue measure of E, and P (E) denotes its distributional perimeter, see [3, Chapter 3]. In order t...
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