Uniformly Positive Scalar Curvature on Manifold Interiors

@misc{chen2026uniformly,
  title = {{Uniformly Positive Scalar Curvature on Manifold Interiors}},
  author = {Shuli Chen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07608},
  eprint = {2610.07608},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07608},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Uniformly Positive Scalar Curvature on Manifold Interiors
AU  - Shuli Chen
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.07608
UR  - https://arxiv.org/abs/2610.07608
AB  - We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on the interiors of certain 4-manifolds using Seiberg--Witten theory. In particular, no punctured blowups of a homotopy K3 manifold admit complete metrics of uniformly positive scalar curvature. Further, let X be a compact oriented smooth manifold of dimension $5$, $6$, or $7$. We show that if IntX admits a complete metric of uniformly positive scalar curvature, then X admits a positive scalar curvature metric with minimal boundary. In dimensions $6$ and $7$, the metric may moreover be chosen to be a product near the boundary. In dimension 5, under additional hypotheses and after possibly changing the smooth structure on X, one can likewise obtain a positive scalar curvature metric that is a product near the boundary.
ER  -