preprint

Inserted: 12 nov 2024
Last Updated: 1 may 2025

Year: 2024

Abstract:

We prove that quasiminimal sets of codimension one in $\mathbf{R}^2$ and $\mathbf{R}^3$ separate a locally finite family of local John domains. Conversely, we show that this condition implies quasiminimality in every dimension. We further prove that quasiminimal sets locally divide the space into two components, except at isolated points in $\mathbf{R}^2$ or outside a subset of dimension strictly less than $N-1$ in $\mathbf{R}^N$.

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• quasiminimalsets_V3.pdf