Year: 2026
Type: preprint
Abstract: We obtain several constructions of uniformly positive scalar curvature complete Riemannian metrics on open manifolds. For dimension $n\geq4$, we show that if such a manifold admits a proper Morse function $f$ bounded below, such that $f$ has no critical points of index $\geq n-2$, then it admits a uniformly positive scalar curvature metric. If a manifold of dimension $4 \leq n\leq 7$ 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.
Source: arXiv (Cornell University)
Author: Das, Anushree
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165392578