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The Airborne Internet is envisioned to be a large scale multihop wireless mesh network of commercial passenger aircraft connected via long range highly directional air-to-air radio links. We propose a localized geographic load sharing technique to mitigate congestion in this network, taking into account the underlying link scheduling constraints with directional antennas. When forwarding packets for a given destination, a node considers not one but a set of next hop candidates, and spreads traffic among them based on queue dynamics. Our simulations show that introducing this flexibility in the routing function can greatly increase a node's ability to satisfy its bandwidth demands during link scheduling, yielding significant performance improvements in terms of network throughput and average packet delay.