Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group

We investigate the optimal Bianchi-Egnell-type quantitative stability constant for the critical nonlocal Sobolev inequality on the Heisenberg group $\mathbb{H}^{n}$, \begin{equation}\label{nS} S_{HL}(Q,μ)\left(\int_{\mathbb{H}^{n}}\int_{\mathbb{H}^{n}} \frac{|u(ξ)|^{Q^{\ast}_μ}|u(η)|^{Q^{\ast}_μ