A graph Γ asymptotic to a regular 2-tree with L = 3; the edge boundary ∂ e Γ0 has 4 edges.
A regular tree with q = 2 and some level sets of a Busemann function.
The surface S, the map from S to , and the double cover of S 0 over I q .
A simple example with strictly larger than K.
Changing the graph with ν = 0 into : the dashed edges are the new edges, the continuous ones the old edges. The picture is done in the same situation as in Figure 6 .
The construction in the proof of Theorem 5.1; for the graph Γ one has q = 3, ν = −1, N′ = N″ = 1, m = 1, M = 5.
The tree , the ball B n−1, and the end T 1 for n = 3.
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