Pith. sign in

REVIEW 1 cited by

Fine Structure of Singularities in Area-Minimizing Currents Mod$(q)$

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2403.15889 v2 pith:PUR6W243 submitted 2024-03-23 math.AP math.DG

classification math.APmath.DG
keywords finetangentconecurrentsflatpointssingularunique
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We study fine structural properties related to the interior regularity of $m$-dimensional area minimizing currents mod$(q)$ in arbitrary codimension. We show: (i) the set of points where at least one tangent cone is translation invariant along $m-1$ directions is locally a connected $C^{1,\beta}$ submanifold, and moreover such points have unique tangent cones; (ii) the remaining part of the singular set is countably $(m-2)$-rectifiable, with a unique flat tangent cone (with multiplicity) at $\mathcal{H}^{m-2}$-a.e. flat singular point. These results are consequences of fine excess decay theorems as well as almost monotonicity of a universal frequency function.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes

    math.DG 2025-07 accept novelty 8.0 of 10

    Near a multiplicity-two plane, a stationary integral varifold with a topological separation condition in flat low-density cylinders is a generalized C^{1,alpha} two-valued graph with unique tangent cones.

Pith tools