Lower bound for the canonical height on abelian varieties over totally p-adic extensions

Let $A/\mathbb{Q}$ be an abelian variety and let $\hat{h}$ be the canonical height on $A(\overline{\Q})$ associated to a symmetric ample line bundle $\mathcal{L}$ on $A$. We prove that $\hat h$ is bounded away from zero on non-torsion points of $A$ defined over the maximal totally $p$-adic extension