Title: Bessel Periods on $U(2,1) \times U(1,1)$, Relative Trace Formula and Non-Vanishing of Central L-values

Abstract: In this paper, we calculate the asymptotics of the second moment of Bessel periods associated to holomorphic discrete series $(\pi,\pi')$ on $U(2,1)\times U(1,1)$ (averaged over $\pi$). Using these, we obtain quantitative non-vanishing results for the Rankin-Selberg central values $L(1/2,\pi\times\pi')$ which arise in the Gan-Gross-Prasad conjectures.