Starting from transportation models for branching structures, we define a function that represents the elevation of the landscape in a river basin. This function is already well-known in the geophysical community but it is only considered under a very strong discretization. We generalize it to the continuous case and study its properties, providing several applications.
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Filippo Santambrogio, Optimal channel networks, landscape function and branched transport. Interfaces Free Bound. 9 (2007), no. 1, pp. 149–169DOI 10.4171/IFB/160