Real Algebraic and Analytic Geometry

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3. Josť F. Fernando:
Analytic surface germs with minimal Pythagoras number.


Submission: 2002, April 25.

We determine all complete intersection surface germs whose Pythagoras number is 2, and find they are all embedded in R^3 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 R^3. Finally, we find in higher embedding dimension three different families with these same properties.

Mathematics Subject Classification (2000): 11E25, 14P15.

Keywords and Phrases: Pythagoras number, mixed and unmixed surface germs, sums of squares.

Full text, 33p.: dvi 148k, ps.gz 108k, pdf 268k.

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