## On the cancellation of singularities of integrable CR-functions.(Russian)Zbl 0648.32008

This article gives a following removability theorem for CR functions analogous to Riemann’s classical theorem on removable singularity for holomorphic functions: Let $$\Gamma =\{\rho_ 1(z)=...=\rho_ k(z)=0\}$$ be a generic CR manifold of class C 3. Let $$\phi$$ be a Hölder continuous CR function, and let f be a locally integrable function on $$\Gamma$$ which is a CR function outside $$K=\{\phi (z)=0\}$$. If the Hessian of $$x_ 1\rho_ 1+...+x_ k\rho_ k$$ is non-degenerate for $$\forall (x_ 1,...,x_ k)\neq 0$$, then f is in fact a CR function on $$\Gamma$$. It also gives a global variant when $$k=1$$ and $$\Gamma$$ is the boundary of a domain $$\Omega\subset {\mathbb{C}}^ 2.$$
Reviewer: A.Kaneko

### MSC:

 32D20 Removable singularities in several complex variables 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators 35N15 $$\overline\partial$$-Neumann problems and formal complexes in context of PDEs

### Keywords:

CR functions; removable singularity
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