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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.

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Authors and Affiliations

  1. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil

    Fernando C. Marques

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  1. Fernando C. Marques
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Correspondence to Fernando C. Marques.

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Marques, F.C. Isolated singularities of solutions to the Yamabe equation. Calc. Var. 32, 349–371 (2008). https://doi.org/10.1007/s00526-007-0144-3

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  • DOI: https://doi.org/10.1007/s00526-007-0144-3

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