Abstract
We determine all complete intersection surface germs whose Pythagoras number is 2, and find that they are all embedded in ℝ3 and have the property that every positive semidefinite analytic function germ is a sum of squares of analytic function germs. In addition, we discuss completely these properties for mixed surface germs in ℝ3. Finally, we find in higher embedding dimension three different families with these same properties.
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