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arXiv · 1805.09597

The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds

Xuezhang Chen·Yuping Ruan·Liming Sun
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Abstract

The Han-Li conjecture states that: Let $(M,g_0)$ be an $n$-dimensional $(n\geq 3)$ smooth compact Riemannian manifold with boundary having positive (generalized) Yamabe constant and $c$ be any real number, then there exists a conformal metric of $g_0$ with scalar curvature $1$ and boundary mean curvature $c$. Combining with Z. C. Han and Y. Y. Li's results, we answer this conjecture affirmatively except for the case that $n\geq 8$, the boundary is umbilic, the Weyl tensor of $M$ vanishes on the boundary and has a non-zero interior point.

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Xuezhang Chen, Yuping Ruan, Liming Sun. 2018-05-24. The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds. https://arxiv.org/abs/1805.09597

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