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Uniqueness of the Cheeger set of a convex body. (English) Zbl 1221.35171
Summary: We prove that if \(C \subset \mathbb R^N\) is of class \(C^2\)and uniformly convex, the Cheeger set of \(C\) is unique. The Cheeger set of \(C\) is the set that minimizes, inside \(C\), the ratio of perimeter over volume.

MSC:
35J70 Degenerate elliptic equations
49J40 Variational inequalities
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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