Blow-up phenomena for the Yamabe equation II

TL;DR

This paper constructs a smooth metric on spheres of dimensions 25 to 51 where the set of constant scalar curvature metrics in its conformal class is non-compact, illustrating blow-up phenomena in geometric analysis.

Contribution

It provides explicit examples of metrics exhibiting non-compactness of the solution space for the Yamabe problem in high dimensions.

Findings

Existence of non-compact solution sets for the Yamabe equation in specified dimensions.

Demonstration of blow-up phenomena for scalar curvature metrics.

Extension of previous results to higher-dimensional spheres.

Abstract

Let n be an integer such that 25 \leq n \leq 51. We construct a smooth metric g on S^n with the property that the set of constant scalar curvature metrics in the conformal class of g is not compact.