Isolated singularities of solutions to the Yamabe equation

Fernando C. Marques

doi:10.1007/s00526-007-0144-3

Isolated singularities of solutions to the Yamabe equation

Fernando C. Marques

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

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 language	English (US)
Pages (from-to)	349-371
Number of pages	23
Journal	Calculus of Variations and Partial Differential Equations
Volume	32
Issue number	3
DOIs	https://doi.org/10.1007/s00526-007-0144-3
State	Published - Jul 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s00526-007-0144-3

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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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AB - 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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JO - Calculus of Variations and Partial Differential Equations

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ER -

Isolated singularities of solutions to the Yamabe equation

Abstract

All Science Journal Classification (ASJC) codes

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