The [`(¶)]-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in \mathbbCPn with n ³ 3

• Autores: Jianguo Cao, Mei-Chi Shaw
• Localización: Mathematische zeitschrift, ISSN 0025-5874, Vol. 256, Nº. 1, 2007, págs. 175-192
• Idioma: inglés
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• Resumen

  • In this paper we study the Cauchy¿Riemann equation in complex projective spaces. Specifically, we use the modified weight function method to study the -Neumann problem on pseudoconvex domains in these spaces. The solutions are used to study function theory on pseudoconvex domains via the -Cauchy problem. We apply our results to prove nonexistence of Lipschitz Levi-flat hypersurfaces in complex projective spaces of dimension at least three, which removes the smoothness requirement used in an earlier paper of Siu