Cheeger-Goreski-MacPherson's conjecture for the varieties with isolated singularities.
On the extension of L2 holomorphic functions III: negligible weights.
On the L2 cohomology of complex spaces.
Addendum to: A Reduction Theorem for Cohomology Groups of Very Strongly q-Convex Kähler Manifolds.
A Reduction Theorem for Cohomology Groups of Very Strongly q-convex Kähler Manifolds.
On the Hyperbolicity of Certain Planar Domains.
∂̅-cohomology and geometry of the boundary of pseudoconvex domains
In 1958, H. Grauert proved: If D is a strongly pseudoconvex domain in a complex manifold, then D is holomorphically convex. In contrast, various cases occur if the Levi form of the boundary of D is everywhere zero, i.e. if ∂D is Levi flat. A review is given of the results on the domains with Levi flat boundaries in recent decades. Related results on the domains with divisorial boundaries and generically strongly pseudoconvex domains are also presented. As for the methods, it is explained how Hartogs...
Hartogs type extension theorems on some domains in Kähler manifolds
Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact Kähler and...
On the parameter dependence of solutions to the ...-equation.
Hodge Spectral Sequence on Pseudoconvex Domains.
A Levi Problem on Two-Dimensional Complex Manifolds.
On the Extension of L2 Holomorphic Functions.
On the real analytic Levi flat hypersurfaces in complex tori of dimension two
We compute the Levi form of the logarithm of the distance function for real hypersurfaces in two dimensional complex tori, and discuss the characterization of Levi flat hypersurfaces there.
The Bergman Kernel on Uniformly Extendable Pseudoconvex Domains.
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