Sharp quantitative stability estimates for critical points of fractional Sobolev inequalities

By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates for critical points of the fractional Sobolev inequalities induced by the embedding ${\dot{H}}^s({\mathbb{R}}^n)\hookrightarrow L^{\frac{2n}{n-2s}}({\mathbb{R}}^n)$ in the whole range of $s\in (0,\frac{n}{2})$.