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In this paper we study the boundary at infinity of the curve complex$\mathcal{C}(S)$ of a surface $S$ of finite type and the relativeTeichm\"{u}ller space $\mathcal{T}_{el}(S)$ obtained from the Teichm\"{u}llerspace by collapsing each region where a simple closed curve is short to be aset of diameter 1. $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ arequasi-isometric, and Masur-Minsky have shown that $\mathcal{C}(S)$ and$\mathcal{T}_{el}(S)$ are hyperbolic in the sense of Gromov. We show that theboundary at infinity of $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ is the spaceof topological equivalence classes of minimal foliations on $S$.

The Boundary at Infinity of the Curve Complex and the Relative Teichm\"{u}ller Space