60 research outputs found
Vanishing Cycles in Holomorphic Foliations by Curves and Foliated Shells
The purpose of this paper is the study of vanishing cycles in holomorphic
foliations by complex curves on compact complex manifolds. The main result
consists in showing that a vanishing cycle comes together with a much richer
complex geometric object - we call this object a foliated shell.Comment: 65 pages, 9 figures. A Section about pluriexact foliatins added. To
appear in GAF
Banach Analytic Sets and a Non-Linear Version of the Levi Extension Theorem
We prove a certain non-linear version of the Levi extension theorem for
meromorphic functions. This means that the meromorphic function in question is
supposed to be extendable along a sequence of complex curves, which are
arbitrary, not necessarily straight lines. Moreover, these curves are not
supposed to belong to any finite dimensional analytic family. The conclusion of
our theorem is that nevertheless the function in question meromorphically
extends along an (infinite dimensional) analytic family of complex curves and
its domain of existence is a pinched domain filled in by this analytic family.Comment: 19 pages, This is the final version with significant corrections and
improvements. To appear in Arkiv f\"or matemati
Schwarz Reflection Principle, Boundary Regularity and Compactness for J-Complex Curves
We establish the Schwarz Reflection Principle for -complex discs attached
to a real analytic -totally real submanifold of an almost complex manifold
with real analytic . We also prove the precise boundary regularity and
derive the precise convergence in Gromov compactness theorem in
\calc^{k,\alpha}-classes.Comment: 21 page
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