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

## TL;DR

This paper investigates the blow-up phenomena in solutions to the constant scalar curvature and boundary mean curvature equation, extending known counterexamples to higher dimensions and analyzing solution compactness.

## Contribution

It extends the existence of counterexamples for solution non-compactness to dimensions not less than 35, improving previous results for dimensions 62 and above.

## Key findings

- Counterexamples exist for dimensions ≥35.
- Solution compactness fails in high dimensions.
- Extends previous results by Chen and Wu.

## 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.