| Abstract: |
| The classical Sobolev inequality in $\mathbb{R}^n$ states that the $L^{\frac{2n}{n-2}}$-norm of smooth compactly supported functions can be controlled, up to an optimal constant $S,$ by the $L^2$-norm of their gradient. The explicit value of $S$ is known, and the cases where equality holds have been obtained and classified as {\it Aubin-Talenti bubbles.}
The question of quantitative stability and its applications has garnered significant interest in recent times.
In this presentation, we will explain the question of the stability of the optimizers and their counterparts within the framework of the hyperbolic space. |
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