| Abstract: |
| In this talk, I will discuss the sharp quantitative stability estimates for nonnegative functions near the solution set of the Yamabe problem on a smooth closed Riemannian manifold $(M,g)$ of dimension $N \ge 3$ which is not conformally equivalent to $\S^N$.
For $3 \le N \le 5$, our result is consistent with the result of Figalli and Glaudo (2020) on $\S^N$.
In the case of $N \ge 6$, we investigate the single-bubbling phenomenon on generic Riemannian manifolds $(M,g)$. Surprisingly, numerological (specifically, the dimension $N$) and geometric effects occur in such a way that they may cause the sharp exponent to become much less than 1.This exhibits a striking difference from the result of Ciraolo, Figalli, and Maggi (2018) on $\S^N$. This work is in collaboration with Seunghyeok Kim. |
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