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Positive Scalar Curvature Obstructions via Singular Dimension Descent

  • Yuchen Bi
  • Jintian Zhu
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Abstract

In light of recent advances in conformal blow-up methods for the positive mass theorem, including He--Shi--Yu, Bi--Hao--He--Shi--Zhu, and Brendle--Wang, we develop a Schoen--Yau type singular dimension descent method for positive scalar curvature obstructions in arbitrary dimensions. We prove obstructions to positive scalar curvature on enlargeable manifolds and establish the corresponding cubical width inequalities and two-systole estimates. The method also applies to enlargeable AM--PI spaces, giving a positive scalar curvature obstruction when the singular set has Assouad codimension greater than 3−2/n.

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Cite

BibTeXRIS
BibTeX
@misc{bi2026positive,
  title = {{Positive Scalar Curvature Obstructions via Singular Dimension Descent}},
  author = {Yuchen Bi and Jintian Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.20528},
  eprint = {2606.20528},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.20528},
}
RIS
TY  - UNPB
TI  - Positive Scalar Curvature Obstructions via Singular Dimension Descent
AU  - Yuchen Bi
AU  - Jintian Zhu
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2606.20528
UR  - https://arxiv.org/abs/2606.20528
AB  - In light of recent advances in conformal blow-up methods for the positive mass theorem, including He--Shi--Yu, Bi--Hao--He--Shi--Zhu, and Brendle--Wang, we develop a Schoen--Yau type singular dimension descent method for positive scalar curvature obstructions in arbitrary dimensions. We prove obstructions to positive scalar curvature on enlargeable manifolds and establish the corresponding cubical width inequalities and two-systole estimates. The method also applies to enlargeable AM--PI spaces, giving a positive scalar curvature obstruction when the singular set has Assouad codimension greater than 3−2/n.
ER  -