Monotonicity of the perimeter with respect to inclusion is well known for bounded convex sets in the plane. Here we give a quantitative estimate for the difference of the perimeters: it shows how much the perimeter of B increases when B becomes larger and larger with respect to some fixed E. We give an example showing that our estimate is sharp.
A Sharp Quantitative Estimate for the Perimeters of Convex Sets in the Plane
LEONETTI, Francesco;
2015-01-01
Abstract
Monotonicity of the perimeter with respect to inclusion is well known for bounded convex sets in the plane. Here we give a quantitative estimate for the difference of the perimeters: it shows how much the perimeter of B increases when B becomes larger and larger with respect to some fixed E. We give an example showing that our estimate is sharp.File in questo prodotto:
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