The Arctic region is a strategic priority for the U.S.. It has been for a long time. Trump has pointed out that China, Russia, and possibly other U.S. adversaries are already active in the region and can threaten U.S. national security. He is also right in pointing out that not enough has been done to guarantee American presence and security in the Arctic and in Greenland. But that is not the fault of Denmark or Greenland. And "owning" Greenland isn't the answer to solving the problem. 

Past U.S. administrations had little interest in securing a foothold of any kind in Greenland. Trump could do so and he could do it without alienating or losing the support of fellow NATO allies. A 1951 treaty with Denmark, which was amended as late as 2004 provides all the legal basis the U.S. needs to structure an agreement to keep NATO allies like Denmark and others strongly supportive of any result. Past administrations walked away from using Greenland for security opportunities, Trump grasps its importance. 

For much of the Cold War, the U.S. had multiple military installations and as many as 6,000 troops there. Prior U.S. administrations, not Denmark, deprioritized Greenland, withdrew U.S. forces, closed bases, and ignored American security in the Arctic. The U.S. now has one base and approximately 150 troops in Greenland. This is a result of America's own decisions and actions. Denmark has maintained some installations America abandoned and can make any future arrangements needed to accommodate an increase in American forces. It has increased its own spending and presence in the Arctic, due to its own security needs, and partly because of American withdrawals. 

The Trump administration could develop a plan for securing the Arctic to include a larger military footprint. It could coordinate with Denmark to provide host-nation support. He could then go to Congress and seek funding to significantly expand America's military influence in the Arctic region. 

Trump's notion that the U.S. needs to "own" Greenland to establish its presence is misplaced. It is also not without problems. Seizing the territory of a NATO ally would undoubtedly cause a fracture and perhaps destroy NATO. NATO is also a strategic alliance the US needs. The NATO alliance has created the largest expanse of free, law-abiding, prosperous territory on earth, all of which is allied with the US. If the US were to become the party threatening the territory of a fellow ally, the alliance would be irrevocably damaged. 

If Denmark and the Greenlanders saw the U.S. as an eager ally as opposed to a hostile political takeover, US investments in Greenland would be welcomed, opening access to vast natural resources. Doing this as a security and business maneuver instead of a political move would avoid the wounds that a takeover would entail.