PreprintarXiv licencearXiv
Counterexamples to prescribed scalar curvature in the null case
Abstract
We construct smooth functions on the flat torus šnā„5 that change sign and have negative mean but cannot be realized as the scalar curvature of any metric in the given conformal class.
Related
- Remarks on prescribed scalar curvature functions
- Complete conformal metrics of constant positive scalar curvature with prescribed isolated singularities
- Finitely many solutions for the prescribed scalar curvature problem at the critical flatness order
- Interior curvature estimates for convex solutions of a prescribed curvature quotient equation
- Regularity for the prescribed vertical mean curvature system in the plane
BibTeX
@misc{li2026counterexamples,
title = {{Counterexamples to prescribed scalar curvature in the null case}},
author = {Yuxiang Li and Yunqing Wu and Jie Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18432},
eprint = {2610.18432},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18432},
}
RIS
TY - UNPB
TI - Counterexamples to prescribed scalar curvature in the null case
AU - Yuxiang Li
AU - Yunqing Wu
AU - Jie Zhou
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18432
UR - https://arxiv.org/abs/2610.18432
AB - We construct smooth functions on the flat torus š^nā„5 that change sign and have negative mean but cannot be realized as the scalar curvature of any metric in the given conformal class.
ER -