Asymptotic behavior of solutions to the σk-Yamabe equation near isolated singularities

Zheng Chao Han, Yan Yan Li, Eduardo V. Teixeira

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


σk-Yamabe equations are conformally invariant equations generalizing the classical Yamabe equation. In (J. Funct. Anal. 233: 380-425, 2006) YanYan Li proved that an admissible solution with an isolated singularity at 0∈ℝn to the σk-Yamabe equation is asymptotically radially symmetric. In this work we prove that such a solution is asymptotic to a radial solution to the same equation on ℝn{set minus}{0}. These results generalize earlier pioneering work in this direction on the classical Yamabe equation by Caffarelli, Gidas, and Spruck. In extending the work of Caffarelli et al., we formulate and prove a general asymptotic approximation result for solutions to certain ODEs which include the case for scalar curvature and σk curvature cases. An alternative proof is also provided using analysis of the linearized operators at the radial solutions, along the lines of approach in a work by Korevaar, Mazzeo, Pacard, and Schoen.

Original languageEnglish (US)
Pages (from-to)635-684
Number of pages50
JournalInventiones Mathematicae
Issue number3
StatePublished - Dec 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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