But, neither Bush nor Obama was able to get the Senate to ratify UNCLOS, so the US has no input thru UNCLOS.
So, Bush and Obama say the ridge is in international waters and the overlapping claims made Canada, Denmark, and Russia are false claims, but we have no way to argue that because we haven't ratified the treaty.
Rather than think that Russia will militarily assert their claim over the ridge, you should also consider that Canada, Denmark, and Russia could negotiate a settlement on how they would split up the ridge among themselves, and get UNCLOS approval of the deal.
Faced with those prospects, Bush sought to negotiate the Arctic within the Arctic Council and Obama has continued with that.
Similarly, Bush sought to negotiate the Antarctic within the OAS and the South China Sea within ASEAN, and Obama has continued along those lines.
The best solution would be to ratify UNCLOS.
I think the UNCLOS has too many New World Socialist Order provisions in it giving the UN way too much power.