Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu)
Pak Tung Ho, Jinwoo Shin
公開日: 2025/8/29
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.