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The topography of tectonically active mountain ranges reflects a poorly understood competition between bedrock uplift and erosion. Dating of abandoned river-cut surfaces in the northwestern Himalayas reveals that the Indus river incises through the bedrock at extremely high rates (2–12 mm yr^-1). In the surrounding mountains, the average angles of hillslopes are steep and essentially independent of erosion rate, suggesting control by a common threshold process. In this rapidly deforming region, an equilibrium is maintained between bedrock uplift and river incision, with landsliding allowing hillslopes to adjust efficiently to rapid river down-cutting.