On the H. Lewy extension phenomenon

Nirenberg, Ricardo

doi:10.1090/S0002-9947-1972-0301234-4

On the H. Lewy extension phenomenon
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Trans. Amer. Math. Soc. 168 (1972), 337-356 Request permission

Abstract:

We prove local approximation and extension theorems for ${C^\infty }$ submanifolds $M$ of ${C^n}$ (CR submanifolds). Under some conditions on $M$, any smooth solution of the induced Cauchy-Riemann equations can be extended holomorphically to bigger (and sometimes open) sets.

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