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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月23日

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  • Pak Tung Ho,
  • Jinwoo Shin

摘要

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.