The local twisted Gan-Gross-Prasad conjecture for $\text{U}(V_K)\mathrm{/}\text{U}(V)$

In this paper, we obtain geometric expansions of a local trace formula and its twisted variant for the twisted Gan-Gross-Prasad conjecture. As an application, we prove the local twisted Gan-Gross-Prasad conjecture for $U(V_K)\mathrm{/}U(V)$ for tempered $L$-parameters over nonarchimedean fields of odd residual characteristic.