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A new reverse isoperimetric inequality and its stability. (English) Zbl 1257.52005

The author deals with the reverse isoperimetric inequality for a closed and strictly convex curve in the Euclidean plane \(\mathbb R^2\) involving the following geometric functionals associated to the given convex curve: length, areas of the region, respectively, included by the curve and the locus of curvature centers, and the integral of the radius of curvature. He also investigates the stability property of such an inequality.

MSC:

52A40 Inequalities and extremum problems involving convexity in convex geometry
52A38 Length, area, volume and convex sets (aspects of convex geometry)
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