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The d-bar-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in CP^n with n>= 3

Jianguo Cao·Mei-Chi Shaw
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Abstract

A Lipschitz hypersurface is a hypersurface which locally is the graph of a Lipschitz function. A Lipschitz (or C^1) hypersurface is said to be Levi-flat if it is locally foliated by complex manifolds of complex dimension (n-1). We shall prove that there exist no Lipschitz Levi-flat hypersurfaces in CP^n with n >= 3. Our new estimates on the d-bar-Cauchy problems are different from the earlier Siu's integral kernal method.

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Jianguo Cao, Mei-Chi Shaw. 2006-10-13. The d-bar-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in CP^n with n>= 3. https://arxiv.org/abs/math/0604112

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