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arXiv · 2504.20587

Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds

Stefano Nardulli·Aldo Pratelli
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Abstract

We prove that in a compact Riemannian manifold, the $m$-minimal clusters of sufficiently small total volume are connected and with small diameter, while in a more general Finsler manifold they are done by at most $m$ connected components of small diameter. We apply these results to calculate the asymptotic expansion of the multi-isoperimetric profile at the first nontrivial order, for small volumes.

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Stefano Nardulli, Aldo Pratelli. 2025-04-29. Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds. https://arxiv.org/abs/2504.20587

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