Generic regularity for minimizing hypersurfaces in dimension 11

Fuente: arXiv
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Main Authors: Chodosh, Otis, Mantoulidis, Christos, Schulze, Felix, Wang, Zhihan
Format: Preprint
Published: 2025
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author Chodosh, Otis
Mantoulidis, Christos
Schulze, Felix
Wang, Zhihan
author_facet Chodosh, Otis
Mantoulidis, Christos
Schulze, Felix
Wang, Zhihan
contents We prove that area-minimizing hypersurfaces are generically smooth in ambient dimension $11$ in the context of the Plateau problem and of area minimization in integral homology. For higher ambient dimensions, $n+1 \geq 12$, we prove in the same two contexts that area-minimizing hypersurfaces have at most an $n-10-ε_n$ dimensional singular set after an arbitrarily $C^\infty$-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively.
format Preprint
id arxiv_https___arxiv_org_abs_2506_12852
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Generic regularity for minimizing hypersurfaces in dimension 11
Chodosh, Otis
Mantoulidis, Christos
Schulze, Felix
Wang, Zhihan
Differential Geometry
Analysis of PDEs
We prove that area-minimizing hypersurfaces are generically smooth in ambient dimension $11$ in the context of the Plateau problem and of area minimization in integral homology. For higher ambient dimensions, $n+1 \geq 12$, we prove in the same two contexts that area-minimizing hypersurfaces have at most an $n-10-ε_n$ dimensional singular set after an arbitrarily $C^\infty$-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively.
title Generic regularity for minimizing hypersurfaces in dimension 11
topic Differential Geometry
Analysis of PDEs
url https://arxiv.org/abs/2506.12852