arXiv Open Access 2024

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

Camillo De Lellis Paul Minter Anna Skorobogatova

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Abstrak

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 $C^{1,β}$ 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.

Topik & Kata Kunci

math.AP math.DG

Penulis (3)

Camillo De Lellis

Paul Minter

Anna Skorobogatova

Format Sitasi

APA MLA BibTeX

Lellis, C.D., Minter, P., Skorobogatova, A. (2024). Fine Structure of Singularities in Area-Minimizing Currents Mod$(q)$. https://arxiv.org/abs/2403.15889

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓