Regularity of branched stable minimal immersed hypersurfaces

@misc{wang2026regularity,
  title = {{Regularity of branched stable minimal immersed hypersurfaces}},
  author = {Gaoming Wang and Xuwen Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.29632},
  eprint = {2607.29632},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.29632},
}

TY  - UNPB
TI  - Regularity of branched stable minimal immersed hypersurfaces
AU  - Gaoming Wang
AU  - Xuwen Zhang
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2607.29632
UR  - https://arxiv.org/abs/2607.29632
AB  - We establish a sharp bound on the Hausdorff dimension of the non-branch singular set of branched stable minimal immersed hypersurfaces whose singular sets have locally finite ℋ^n−2-measure: the non-branch singular set is empty when n=2, discrete when n=3, and has Hausdorff dimension at most n−3 when n≥4. We also construct a non-flat stable minimal cone in ℝ^4 arising from a branched minimal immersion whose vertex is a non-branch singularity. Taking products with Euclidean factors yields examples whose non-branch singular sets have Hausdorff dimension exactly n−3, showing that our regularity bound is sharp in every dimension n≥3. The main ingredients in our proof are a generalized Schoen inequality and a corresponding branched sheeting theorem near stationary classical cones and unions of hyperplanes.
ER  -