An isoperimetric inequality for logarithmic capacity of polygons
نویسنده
چکیده
We verify an old conjecture of G. Pólya and G. Szegő saying that the regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area.
منابع مشابه
An isoperimetric inequality for logarithmic capacity
We prove a sharp lower bound of the form capE ≥ (1/2)diamE · Ψ(areaE/((π/4)diam 2E)) for the logarithmic capacity of a compact connected planar set E in terms of its area and diameter. Our lower bound includes as special cases G. Faber’s inequality capE ≥ diamE/4 and G. Pólya’s inequality capE ≥ (areaE/π)1/2. We give explicit formulations, functions of (1/2)diamE, for the extremal domains which...
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