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Isolated singularities of solutions to the Yamabe equation. I.
Jingang Xiong, Beijing Normal University
Date & time: Tuesday, 30 June 2020 at 1:40PM - 3:40PM
Abstract: I will talk about the asymptotic behavior of local solutions to the Yamabe equation near an isolated singularity, when the metric is not locally conformally flat. I will show that when the dimension is less than or equal to 6, any solution is asymptotic to a radially symmetric Fowler solution. This is based on two papers: F. Marques 2008 for dimensions less than 6 and a recent preprint of L. Zhang and myself for dimension 6. When the metric is locally conformally flat, the above mentioned asymptotic behavior holds in all dimensions, which was proved in the classical paper of Caffarelli-Gidas and Spruck 1989. See also an important refinement due to Korevaar, Mazzeo, Pacard and Schoen 1999.