Positive semidefinite analytic functions on real analytic surfaces

Abstract

Let $X\subset {\mathbb{R}}^n$ be a (global) real analytic surface. Then every positive semidefinite meromorphic function on $X$ is a sum of $10$ squares of meromorphic functions on $X$. As a consequence, we provide a real Nullstellensatz for (global) real analytic surfaces.

27 pages

References in corpus (2)

• The Pythagoras number and the $u$-invariant of Laurent series fields in several variables
• Sums of squares in function fields over Henselian local fields

Cited by in corpus (3)

• Sums of squares on hypersurfaces
• On Waring numbers of henselian rings
• Étale cohomology of algebraic varieties over Stein compacta