Almost-everywhere regularity of stationary integral varifolds

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Simon, Introduction to Geometric Measure Theory (2018 notes) evidence for this event

Theorem 1.1: every stationary integral $m$-varifold in an open subset of $\mathbb R^{m+n}$, $m,n\ge1$, has $\mathcal H^m(\mathrm{Sing}\,V)=0$, with no stability, minimizing, orientability, density-bound or codimension hypothesis. Corollary 1.2 gives the same on round spheres. The main new estimate is a signed excess bound in flat cylinders. The companion A Codimension-One Bound for the Singular Set of a Stationary Integral Varifold (5 Oct 2026) claims the stronger bound $\dim_{\mathcal H}\mathrm{Sing}\,V\le m-1$, which implies this one and is a separate entry; it uses this paper's signed-excess theorem as an input. Neither paper treats non-Euclidean ambient metrics, where De Lellis-Hirsch-Lihn-Spolaor construct exotic examples. parent of this event

VibeMathed record: Almost-everywhere regularity of stationary integral varifolds evidence for this event

Almost-everywhere regularity 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

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