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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/9600
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