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


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
Full Text: EuDML