Isolated singularities of solutions to the Yamabe equation in higher dimensions I

Abstract

We complete, in the Riemannian setting, the classification of isolated singularities of positive solutions to the Yamabe equation for \(3\le n\le 29\), initiated in the flat case by Caffarelli, Gidas, and Spruck in 1989. Precisely, every isolated singularity is either removable or asymptotic to a Fowler solution. The sharpness of this range is established by counterexamples for \(n\ge30\) in our subsequent paper.

108 pages