Seven countries, Argentina, Australia, Chile, France, New Zealand, Norway and the United Kingdom, have made territorial claims covering parts of Antarctica, and three of those claims, Argentina's, Chile's and the United Kingdom's, physically overlap the same sector. The 1959 Antarctic Treaty neither recognizes nor cancels any of these claims; it bars any new claim and bars any existing claim from being enlarged while the treaty is in force, leaving the underlying ownership question frozen rather than settled.
What would resolve this Either a new treaty replacing the current freeze with a settled territorial arrangement, or a claimant state formally renouncing its claim, would resolve which of the overlapping claims, if any, holds.
OpenInternational lawTerritorial claims in Antarctica (Wikipedia)