The following blog post poses a challenge to the anarcho-capitalists:
“In the end, current Antarctic territorial claims are only valid as long as they are not challenged. So I ask the anarchists and extreme libertarians, exactly how does one negotiate a territorial claim (or defend their property right) with an unmatchable armed force that happens to be an absolutely necessary miltary ally?”
http://www.macrobusiness.com.au/2011/10/who-really-owns-antarctica/