On the removable singularities of complex analytic sets
There is proved the sufficiency of several conditions for the removability of singularities of complex-analytic sets in domains of $\mathbb C^n$.
math.CV↗
arXiv subjects
E. M. Chirka
Publications and source records attributed to E. M. Chirka.
Large Harnack inequalities, Kobayashi distances and holomorphic motions
We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties of holomorphic motions over almost complex manifolds.
math.CV↗
Radó theorem and its generalization for CR-mappings
The following theorem is proved: Let M be a locally Lipschitz hypersurface in C^n with one-sided extension property at each point (e.g., without analytic discs). Let S be a closed subset of M and f : M \ S ---> C^m \ E is a CR-mapping of class L^{\infty} such that the cluster set of f on S along of Lebesque points of f is contained in a closed complete pluripolar set E. Then there is a CR-mapping f : M ---> C^m of class L^{\infty}(M) such that f |M§= f. It follows also that S is removable for CR \cap L^{\infty} (M \ S).
math.CV↗
On the Removable Singularities for Meromorphic Mappings
If E is a nonempty closed subset of the locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold M and all points of E are nonremovable for a meromorphic mapping of M \ E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of M.
math.CV↗