Isolated singularities of solutions to the Yamabe equation

Marques, Fernando
July 2008
Calculus of Variations & Partial Differential Equations;Jul2008, Vol. 32 Issue 3, p349
Academic Journal
In this paper we study the asymptotic behavior of local solutions to the Yamabe equation near an isolated singularity, when the metric is not necessarily conformally flat. We are able to prove, when the dimension is less than or equal to five, that any solution is asymptotic to a rotationally symmetric Fowler solution. We also prove refined asymptotics if deformed Fowler solutions are allowed in the expansion.


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