According to Hapgood and the Flem-Aths, Lesser Antarctica was outside the Arctic Circle up until the poleshift 10,000 odd years ago. This explains why the thickness of ice is greater in Greater Antarctica.

This doesn't explain the claims of American scientists that the ice in Lesser Antarctica has been steadily melting for the last 10,000 years:

"In a study appearing Friday in the journal Science, researchers say that geochemical measurements of when mountainside rocks first become free of ice near the south pole show that the West Antarctic Ice Sheet began melting about 10,000 years ago and is still shrinking. "

Map at Flem-Ath.com

** Lesser Antarctica is basically the bits closest to South America