Germs of CR maps between real analytic hypersurfaces (Q1107677)

Suppose H is a smooth CR mapping between two real-analytic hypersurfaces M and M' in \({\mathbb{C}}^{n+1}\) and let \(P_ 0\in M\). The authors derive sufficient conditions for H to extend holomorphically to an ambient neighborhood of \(P_ 0\). The conditions are given in terms of algebraic concepts, essential finiteness of M at \(P_ 0\) and M' at \(H(p_ 0)\), and finite multiplicity of H at \(P_ 0\). The techniques are rather algebraic as well, using such results as Nakayama's Lemma, the Nullstellensatz, and the Weierstrass Preparation Theorem.