Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Mingxiang, Ngo, Quoc Anh, Xu, Xingwang
Institutions: Hong Kong Polytechnic University, Nanjing University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221875510