Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds

2025/04/29 by Stefano Nardulli, Nardulli, Stefano, Aldo Pratelli +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2504.20587

openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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