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Regularity of minimizing clusters

This chapter is devoted to the discussion of the regularity properties of minimizing clusters. We shall first prove the following -a.e. regularity result in arbitrary dimension (Theorem 30.1); then, in Section 30.3, we shall focus on the planar case, and achieve a more precise result, including a complete description of near-to-singularities behavior; see Theorem 30.7.

**Theorem 30.1** *If is a minimizing N-cluster in ^{n} and 0 ≤ h < k ≤ N, then (h, k) is an analytic hypersurface with constant mean curvature in ...*

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