Skip to content
DraconiticResearch
Search Sources API
186,625 studies31 sourcesUpdated 19 min ago
PreprintarXiv licencearXiv

Quadratic Scalar Curvature Decay and Uniform Positivity in Dimensions Four through Seven

  • Zhehui Wang
  • Jintian Zhu
Open at sourcePDFDOICite

Abstract

Let 4≤ n≤7 and let (Mn,g) be a complete, connected, orientable, noncompact Riemannian manifold of positive scalar curvature. We prove that if the asymptotic quadratic scalar curvature coefficient of g is greater than (n−1)/n, then M carries a complete smooth metric whose scalar curvature is at least one. The threshold (n−1)/n and the strict inequality are optimal. This confirms the second part of Gromov's critical rate of decay conjecture in dimensions four through seven.

Related

  1. Uniform positive scalar curvature from supercritical quadratic decay
    Zhehui Wang, Jintian Zhu
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. Uniform Quadratic Growth and Second-Order Variational Curvature in Hilbert Spaces
    Samir Adly, Ralph Tyrrell Rockafellar
    HALPreprintCC BY 4.0Full textGeneral mathematicsHAL
  3. From the Optimal L2-Estimates (p,n) and (n,p)-Forms to Uniform Griffiths p-Positivity via Convolution and Restriction
    Zhuo Liu, Xujun Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Individual and Uniform Eventual Positivity of Self-Adjoint Semigroups
    Alexander Dobrick
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. Uniform RC-positivity of tangent bundles
    Chenghao Qing, Hongzhao Sun, Xiangyu Zhou
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{wang2026quadratic,
  title = {{Quadratic Scalar Curvature Decay and Uniform Positivity in Dimensions Four through Seven}},
  author = {Zhehui Wang and Jintian Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03676},
  eprint = {2609.03676},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03676},
}
RIS
TY  - UNPB
TI  - Quadratic Scalar Curvature Decay and Uniform Positivity in Dimensions Four through Seven
AU  - Zhehui Wang
AU  - Jintian Zhu
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.03676
UR  - https://arxiv.org/abs/2609.03676
AB  - Let 4≤ n≤7 and let (M^n,g) be a complete, connected, orientable, noncompact Riemannian manifold of positive scalar curvature. We prove that if the asymptotic quadratic scalar curvature coefficient of g is greater than (n−1)/n, then M carries a complete smooth metric whose scalar curvature is at least one. The threshold (n−1)/n and the strict inequality are optimal. This confirms the second part of Gromov's critical rate of decay conjecture in dimensions four through seven.
ER  -