Isolated singularities of solutions to the Yamabe equation

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)349-371
Number of pages23
JournalCalculus of Variations and Partial Differential Equations
Volume32
Issue number3
DOIs
StatePublished - Jul 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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