A Note On The Isoperimetric Inequality And Its Stability

Details A Note On The Isoperimetric Inequality And Its Stability A Note On The Isoperimetric Inequality And Its Stability

2011-02-28

arxiv.org/abs/1102.5642v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we deals with isoperimetric-type inequalities for closed convex curves in the Euclidean plane R^2. We derive a family of parametric inequalities involving the following geometric functionals associated to a given convex curve with a simple Fourier series proof: length, area of the region included by the curve, area of the domain enclosed by the locus of curvature centers and integral of the radius of curvature. By using our isoperimetric-type inequalities, we also obtain some new geometric Bonnesen-type inequalities. Furthermore we investigate stability properties of such inequalities (near equality implies curve nearly circular).

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