Skin Structures on Minimal Hypersurfaces

2015/12/27 by Joachim Lohkamp, Lohkamp, Joachim
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1512.08249

openalex publication_date 2015/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic properties of such hypersurfaces.

Citations

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

Related

• Skin Structures in Scalar Curvature Geometry
• Singularities of minimal submanifolds
• Hyperbolic Geometry and Potential Theory on Minimal Hypersurfaces
• New examples of higher-dimensional minimal hypersurfaces
• Singular Minimal Hypersurfaces and Scalar Curvature