Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds

Xuezhang Chen; Liming Sun

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arXiv · 1611.00229

Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds

Xuezhang Chen·Liming Sun

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Abstract

We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension $n\geq 3$. We prove the existence of such conformal metrics in the cases of $n=6,7$ or the manifold is spin and some other remaining ones left by Escobar. Furthermore, in the positive Yamabe constant case, by normalizing the scalar curvature to be $1$, there exists a sequence of conformal metrics such that their constant boundary mean curvatures go to $+\infty$.

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Xuezhang Chen, Liming Sun. 2016-11-01. Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds. https://arxiv.org/abs/1611.00229

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