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Uniform positive scalar curvature from supercritical quadratic decay
Abstract
Let (Mn,g) be a complete connected noncompact smooth Riemannian manifold without boundary, with n≥3 and positive scalar curvature. We prove that M admits a complete smooth metric of uniformly positive scalar curvature if liminfdg(o,x)→∞dg(o,x)2Rg(x)>(n−1)/n for a fixed point o∈ M. This extends earlier existence results for orientable manifolds, due to Chen in dimension three and to the authors in dimensions 4≤ n≤7, to every dimension n≥3 without an orientability assumption.
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BibTeX
@misc{wang2026uniform,
title = {{Uniform positive scalar curvature from supercritical quadratic decay}},
author = {Zhehui Wang and Jintian Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05933},
eprint = {2610.05933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05933},
}
RIS
TY - UNPB
TI - Uniform positive scalar curvature from supercritical quadratic decay
AU - Zhehui Wang
AU - Jintian Zhu
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05933
UR - https://arxiv.org/abs/2610.05933
AB - Let (M^n,g) be a complete connected noncompact smooth Riemannian manifold without boundary, with n≥3 and positive scalar curvature. We prove that M admits a complete smooth metric of uniformly positive scalar curvature if liminf_d_g(o,x)→∞d_g(o,x)^2R_g(x)>(n−1)/n for a fixed point o∈ M. This extends earlier existence results for orientable manifolds, due to Chen in dimension three and to the authors in dimensions 4≤ n≤7, to every dimension n≥3 without an orientability assumption.
ER -