Quantitative estimates on the singular set of minimal hypersurfaces with bounded index

DOI10.1007/S12220-024-01822-3MaRDI QIDQ6624060

Paul Minter, Nicolau S. Aiex, Sean McCurdy

Publication date: 24 October 2024

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

singularityMinkowski contentvarifoldfinite index

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20)

Cites Work

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• Cylindrical tangent cones and the singular set of minimal submanifolds
• The singular structure and regularity of stationary varifolds
• A general regularity theory for stable codimension 1 integral varifolds
• Existence of integral \(m\)-varifolds minimizing \(\int |A|^p\) and \(\int |H|^p\), \(p>m\), in Riemannian manifolds
• Regularity of stable minimal hypersurfaces
• Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents
• Morse index, Betti numbers, and singular set of bounded area minimal hypersurfaces

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