Area minimizing sets subject to a volume constraint in a convex set. (English) Zbl 0940.49025

The paper concerns the problem of minimizing the perimeter of subsets of \(\Omega\) (a convex subset of a Euclidean space) subject to a volume constraint. The problem is to determine whether in general a minimizer is convex. It has been proved that if \(\Omega\) satisfies a “great circle” condition, then any minimizer is convex.


49Q10 Optimization of shapes other than minimal surfaces
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
49Q20 Variational problems in a geometric measure-theoretic setting
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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