| Abstract: |
| In this talk, I will first revisit some new progress on the optimal stability of geometric inequality including Sobolev inequality, HLS inequality and fractional Sobolev inequality etc. Then I will present our recent results on the stability of Sobolev inequality and Sobolev equation in the end-point case. Finally, I will explain the relationship between these quantitative stability inequality and Aubin` conjecture, Chang-Yang conjecture, Keller-Segel equation |
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