Some constructions of uniformly positive scalar curvature metrics on open manifolds
Abstract
We obtain several constructions of uniformly positive scalar curvature complete Riemannian metrics on open manifolds. For dimension n≥4, we show that if such a manifold admits a proper Morse function f bounded below, such that f has no critical points of index ≥ n−2, then it admits a uniformly positive scalar curvature metric. If a manifold of dimension 4 ≤ n≤ 7 admits a positive scalar curvature metric along with a compact exhaustion {Ui} such that the boundary of each Ui is minimal, then it also admits a uniformly positive scalar curvature metric. For the same dimensions, we show that if a manifold has product ends and a positive scalar curvature metric with C-quadratic decay at infinity for C>4π2 with respect to some basepoint, then the existence of a certain mean convex slice far enough from the basepoint implies the existence of a uniformly positive scalar curvature metric on the manifold. In particular, manifolds which have a combination of these behaviours also admit a uniformly positive scalar curvature metric. We also study some applications of these results.
Related
- Nonexistence of complete metrics with uniformly positive scalar curvature
- A remark on the compactness of manifolds with non-negative Ricci curvature and uniformly convex boundary
- Uniformly Positive Scalar Curvature on Manifold Interiors
- Complete conformal metrics of constant positive scalar curvature with prescribed isolated singularities
- Torus and Positive Mass stability for metrics with Ricci curvature lower bound
BibTeX
@misc{das2026some,
title = {{Some constructions of uniformly positive scalar curvature metrics on open manifolds}},
author = {Anushree Das},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.19619},
eprint = {2606.19619},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19619},
}
RIS
TY - UNPB
TI - Some constructions of uniformly positive scalar curvature metrics on open manifolds
AU - Anushree Das
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2606.19619
UR - https://arxiv.org/abs/2606.19619
AB - We obtain several constructions of uniformly positive scalar curvature complete Riemannian metrics on open manifolds. For dimension n≥4, we show that if such a manifold admits a proper Morse function f bounded below, such that f has no critical points of index ≥ n−2, then it admits a uniformly positive scalar curvature metric. If a manifold of dimension 4 ≤ n≤ 7 admits a positive scalar curvature metric along with a compact exhaustion {U_i} such that the boundary of each U_i is minimal, then it also admits a uniformly positive scalar curvature metric. For the same dimensions, we show that if a manifold has product ends and a positive scalar curvature metric with C-quadratic decay at infinity for C>4π^2 with respect to some basepoint, then the existence of a certain mean convex slice far enough from the basepoint implies the existence of a uniformly positive scalar curvature metric on the manifold. In particular, manifolds which have a combination of these behaviours also admit a uniformly positive scalar curvature metric. We also study some applications of these results.
ER -