# Conformal curvature flows on compact manifold of negative Yamabe constant

@article{Chen2018ConformalCF,
title={Conformal curvature flows on compact manifold of negative Yamabe constant},
author={Xuezhang Chen and Pak Tung Ho},
journal={Indiana University Mathematics Journal},
year={2018},
volume={67},
pages={537-581}
}
• Published 2018
• Mathematics
• Indiana University Mathematics Journal
Abstract. We study some conformal curvature flows related to prescribed curvature problems on a smooth compact Riemannian manifold (M, g0) with or without boundary, which is of negative (generalized) Yamabe constant, including scalar curvature flow and conformal mean curvature flow. Using such flows, we show that there exists a unique conformal metric of g0 such that its scalar curvature in the interior or mean curvature curvature on the boundary is equal to any prescribed negative smooth…
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