3‐Manifolds With Positive Scalar Curvature and Bounded Geometry
ABSTRACT We show that a complete contractible 3‐manifold with positive scalar curvature and bounded geometry must be . We also show that an open handlebody of genus larger than 1 does not admit complete metrics with positive scalar curvature and bounded geometry. Our results rely on the maximal weak solution to inverse mean curvature flow due to the third‐named author.
Authors
- Otis Chodosh (ORCID: https://orcid.org/0000-0002-6124-7889)
- Kai Xu (ORCID: https://orcid.org/0000-0001-8914-039X)
- T. Lam
Institutions
- Duke University (US)
- University of California, Irvine (US)
- Stanford University (US)
Publication Details
- Journal
- Communications on Pure and Applied Mathematics
- Published
- 2026-01-08
- DOI
- https://doi.org/10.1002/cpa.70029
- Citations
- 1
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 66.32