Pith. sign in

REVIEW 1 cited by

Existence and regularity of min-max anisotropic minimal hypersurfaces

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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 2409.15232 v1 pith:6ADOZ72F submitted 2024-09-23 math.DG math.AP

Guido De Philippis , Antonio De Rosa , Yangyang Li This is my paper
classification math.DGmath.AP
keywords anisotropicmin-maxminimalclosedconstructionmanifoldobtainsmooth
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

In any closed smooth Riemannian manifold of dimension at least three, we use the min-max construction to find anisotropic minimal hyper-surfaces with respect to elliptic integrands, with a singular set of codimension~$2$ vanishing Hausdorff measure. In particular, in a closed $3$-manifold, we obtain a smooth anisotropic minimal surface. The critical step is to obtain a uniform upper bound for density ratios in the anisotropic min-max construction. This confirms a conjecture by Allard [Invent. Math., 1983].

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Min-Max Construction of Anisotropic Minimal Surfaces with Genus Bound

    math.DG 2026-06 unverdicted novelty 8.0 of 10

    Proves convergence and regularity for anisotropic minimal surfaces via isotopy-class min-max methods in 3-manifolds, with removable singularities under ellipticity or C^3-pinching.

Pith tools