Area-minimizing Hypersurfaces in Singular Ambient Manifolds

Yihan Wang

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arXiv · 2406.18235

Area-minimizing Hypersurfaces in Singular Ambient Manifolds

Yihan Wang

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Abstract

We study area-minimizing hypersurfaces in singular ambient manifolds whose tangent cones have nonnegative scalar curvature on their regular parts. We prove that the singular set of the hypersurface has codimension at least 3 in our settings. We also give an example in which n-dimensional minimizing hypersurface in an ambient space as given above may have singularities of dimension $n-3$. This shows that our regularity result is sharp.

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Yihan Wang. 2024-06-26. Area-minimizing Hypersurfaces in Singular Ambient Manifolds. https://arxiv.org/abs/2406.18235

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