Analytic stability of the CR cross-cap

• Autores: Adam Coffman
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 226, Nº 2, 2006, págs. 221-258
• Idioma: inglés
• DOI: 10.2140/pjm.2006.226.221
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• Resumen

  • For m < n, any real analytic m-submanifold of complex n-space with a nondegenerate CR singularity is shown to be locally equivalent, under a holomorphic coordinate change, to a fixed real algebraic variety defined by linear and quadratic polynomials. The situation is analogous to Whitney¿s stability theorem for cross-cap singularities of smooth maps. The complex analyticity of the normalizing transformation is proved using a rapid convergence argument.