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arXiv · 1908.04815

Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation

Xuezhang Chen·Nan Wu
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Abstract

We first present a warped product manifold with boundary to show the non-uniqueness of the positive constant scalar curvature and positive constant boundary mean curvature equation. Next, we construct a smooth counterexample to show that the compactness of the set of "lower energy" solutions to the above equation fails when the dimension of the manifold is not less than $62$.

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Xuezhang Chen, Nan Wu. 2019-08-13. Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation. https://arxiv.org/abs/1908.04815

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