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Cheeger sets for rotationally symmetric planar convex bodies. (English) Zbl 1476.52001

Summary: In this note we obtain some properties of the Cheeger set \(C_{\varOmega}\) associated to a \(k\)-rotationally symmetric planar convex body \(\varOmega\). More precisely, we prove that \(C_{\varOmega}\) is also \(k\)-rotationally symmetric and that the boundary of \(C_{\varOmega}\) touches all the edges of \(\varOmega\).

MSC:

52A10 Convex sets in \(2\) dimensions (including convex curves)
52A40 Inequalities and extremum problems involving convexity in convex geometry
28A75 Length, area, volume, other geometric measure theory

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