Isolated singularities of solutions to the Yamabe equation in dimension $6$

Abstract

We study the asymptotic behavior of local solutions to the Yamabe equation near an isolated singularity, when the metric is not conformally flat. We prove that, in dimension $6$, any solution is asymptotically close to a Fowler solution, which is an extension of the same result for lower dimensions by F.C. Marques in 2008.

20 pages

References in corpus (2)

• Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities
• Singular solutions to the Yamabe equation with prescribed asymptotics

Cited by in corpus (1)

• Local estimates for conformal $Q$-curvature equations