Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \leq H^1(∂B) . Here we give a quantitative estimate of the difference of the perimeters: it shows how much the perimeter of B increases when B becomes larger and larger with respect to E. We give an example showing that our estimate is sharp.

### A sharp quantitative estimate for the perimeters of convex sets in the plane

#### Abstract

Let E ⊂ B ⊂ R 2 be bounded, convex sets. The monotonicity of the perimeters holds, i.e. H^1(∂E) \leq H^1(∂B) . Here we give a quantitative estimate of the difference of the perimeters: it shows how much the perimeter of B increases when B becomes larger and larger with respect to E. We give an example showing that our estimate is sharp.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/619140
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