abstract


For a given finite graph or a finite graph of finite groups, we show that among all metric graphs (of groups) with volume 1, there exists a unique metric minimizing the volume entropy. We describe it completely (and locally) in terms of the valencies of vertices. In the case of regular or biregular graphs, the entropy minimizing metric gives same length to all edges. This is the complete answer to the analogue of Gromov-Katok conjecture for graphs.
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