Trump has eliminated use of military force. He has not eliminated threat of economic force.
A reasonable argument for his wanting possession is that he wants to put in multi $billion installations for military protection. That could be accomplished by 99 year leases on areas of land, with steps to renew after 70 years. Thus nothing would be built without secure land leases. Most commercial property needs major rebuilds and renovation every 30 years. So we would not be stuck with expensive facilities but no legal land claim and timeframe.
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Something similar could also be arranged for exploiting mineral wealth.
How Soviet of him.
Greenland: Soviet satellite
But no tariffs to us. The taxpayers