The codimension-one bound for singular sets of stationary integral varifolds

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The codimension-one bound for singular sets of stationary integral varifolds parent of this event

Companion: Almost-everywhere regularity of stationary integral varifolds (input to this proof) evidence for this event

Brena, Decio, De Lellis, Remarks and conjectures on stationary varifolds (2025) evidence for this event

Theorem 1.1: for every stationary integral $m$-varifold $V$ in an open $U\subset\mathbb R^{m+n}$, $m,n\ge1$, $\dim_{\mathcal H}\mathrm{Sing}\,V\le m-1$, with no stability, minimizing, orientability, density or codimension hypothesis; crossing planes show it is sharp. This implies $\mathcal H^m(\mathrm{Sing}\,V)=0$. The proof combines the companion paper's signed-excess estimates with a fitting and frequency analysis around a smooth center and a measure-valued blow-up at higher-multiplicity planar tangents. It does not prove rectifiability or finer structure of the singular set, and does not cover Riemannian ambient metrics. parent of this event

The codimension-one bound for singular sets of stationary integral varifolds evidence for this event

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