PreprintarXiv licencearXiv
Remarks on prescribed scalar curvature functions
Abstract
This short article is devoted to the study of the positive solution of Yamabe-type semi-linear equation with prescribed coefficient on general closed manifolds. Our main result is to provide some sufficient conditions for the existence of the positive solutions and give some examples to show that those conditions are sharp. An application to scalar-flat manifold settles a long standing question in prescribing scalar curvature problem in negative form.
Related
- Counterexamples to prescribed scalar curvature in the null case
- 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{li2026remarks,
title = {{Remarks on prescribed scalar curvature functions}},
author = {Mingxiang Li and Quoc Anh Ngo and Xingwang Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19667},
eprint = {2610.19667},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19667},
}
RIS
TY - UNPB
TI - Remarks on prescribed scalar curvature functions
AU - Mingxiang Li
AU - Quoc Anh Ngo
AU - Xingwang Xu
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19667
UR - https://arxiv.org/abs/2610.19667
AB - This short article is devoted to the study of the positive solution of Yamabe-type semi-linear equation with prescribed coefficient on general closed manifolds. Our main result is to provide some sufficient conditions for the existence of the positive solutions and give some examples to show that those conditions are sharp. An application to scalar-flat manifold settles a long standing question in prescribing scalar curvature problem in negative form.
ER -