| Abstract: |
| For $s - \frac{n}{2} \in (0,1) \cup (1,2)$, a reverse-type Sobolev inequality of order $2s$ holds on the sphere $\mathbb S^n$. In my talk, I will discuss recent results on the quantitative stability of this inequality. Implementing the classical proof strategy by Bianchi and Egnell is non-trivial here because the underlying operator $A_{2s}$ is not positive definite when $s > \frac{n}{2}$. Remarkably, the case $s - \frac{n}{2} \in (1,2)$ constitutes the first example of a Sobolev-type stability inequality (i) whose best constant is explicit and (ii) which does not admit an optimizer. |
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