2024/06/26 by Wang, Yihan
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2406.18235
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.