An Error Estimate for the Isoperimetric Deficit
نویسنده
چکیده
A four part dissection and rearrangement provides a new proof of the isoperimetric inequality in the plane as well as a new approach to Bonnesen-type error estimates for the isoperimetric deficit of compact convex sets and of star bodies that are centrally symmetric with respect to the origin. An isoperimetric inequality in R bounds the area (or related functional) of a compact set by some function of the perimeter (or related functional) of that same set. The classical isoperimetric inequality asserts that, for any compact subset S ⊆ R having well-defined perimeter,
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