Minimal surfaces in $\mathbb{H}^2\times\mathbb{R}$ with finite total curvature and embedded ends

In this paper we study the global geometry and classification of complete minimal surfaces with embedded ends and finite total curvature in the product space $\mathbb{H}^2 \times \mathbb{R}$. We describe the structure of embedded ends of such surfaces, constraining the combinatorics of their asympto