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arXiv · 2508.21343

Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu)

Pak Tung Ho·Jinwoo Shin
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Abstract

In this paper, the compactness of the solutions to the constant scalar curvature and constant boundary mean curvature equation is considered. Chen and Wu constructed a smooth counterexample showing 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. We prove that a smooth counterexample still exists when the dimension of the manifold is not less than 35.

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Pak Tung Ho, Jinwoo Shin. 2025-08-29. Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu). https://arxiv.org/abs/2508.21343

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