Two countries close to Antarctica, Chile and Argentina, are not signatories to the Antarctic Treaty and have territorial claims. Both of these countries already have a decent amount of natural resource extraction (especially Chile), so one would reason that if it is worth mining, they would be.

https://en.wikipedia.org/wiki/Argentine_Antarctica https://en.wikipedia.org/wiki/Chilean_Antarctic_Territory

One could also look at the interior of Greenland, which is Danish territory. No serious development of any kind occurs there - it's all along the coasts.