PreprintarXiv licencearXiv
A note on the positivity of Q-curvature via the continuity method
Abstract
Suppose $(M, g)$ is a smooth, closed, $5$-dimensional Riemannian manifold with positive Yamabe invariant Y(M, [g]) > 0 and positive Yamabe-type Q-curvature invariant Y4∗(M, [g]) > 0. Using the continuity method, we prove the existence of a metric in the conformal class [g] with positive scalar curvature and positive Q-curvature, assuming an additional condition on an ``initial metric" in the class [g].
Related
- A Note on Universal Positivity of Rank-Two Quantum Greedy Elements
- Positivity and Continuity of Lyapunov Exponents for Multi-Frequency Skew-Shift Schrödinger Operators
- Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature
- Prescribed combinatorial curvature beyond positivity for spherical vertex scalings on the sphere
- Wronskian curvature positivity is equivalent to the existence of a holomorphic projective connection
BibTeX
@misc{mete2026note,
title = {{A note on the positivity of $Q$-curvature via the continuity method}},
author = {Ramesh Mete},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28234},
eprint = {2608.28234},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28234},
}
RIS
TY - UNPB
TI - A note on the positivity of Q-curvature via the continuity method
AU - Ramesh Mete
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28234
UR - https://arxiv.org/abs/2608.28234
AB - Suppose $(M, g)$ is a smooth, closed, $5$-dimensional Riemannian manifold with positive Yamabe invariant Y(M, [g]) > 0 and positive Yamabe-type Q-curvature invariant Y_4^∗(M, [g]) > 0. Using the continuity method, we prove the existence of a metric in the conformal class [g] with positive scalar curvature and positive Q-curvature, assuming an additional condition on an ``initial metric" in the class [g].
ER -