135 research outputs found
Regularity and estimates for -holomorphic discs attached to a maximal totally real submanifold
We prove that pseudo-holomorphic discs attached to a maximal totally real
submanifold inherit their regularity from the regularity of the submanifold and
of the almost complex structure. The proof is based on the computation of an
explicit lower bound for the Kobayashi metric in almost complex manifolds,
which also yields explicit estimates of H\"olderian norms of such discs.Comment: 20 pages, 2 figure
The role of Fourier modes in extension theorems of Hartogs-Chirka type
We generalize Chirka's theorem on the extension of functions holomorphic in a
neighbourhood of graph(F)\cup(\partial D\times D) -- where D is the open unit
disc and graph(F) denotes the graph of a continuous D-valued function F -- to
the bidisc. We extend holomorphic functions by applying the Kontinuitaetssatz
to certain continuous families of analytic annuli, which is a procedure suited
to configurations not covered by Chirka's theorem.Comment: 17 page
Overinterpolation
In this paper we study the consequences of overinterpolation, i.e., the
situation when a function can be interpolated by polynomial, or rational, or
algebraic functions in more points that normally expected. We show that in many
cases such a function has specific forms.Comment: 14 page
On the removable singularities for meromorphic mappings
If is a closed subset of locally finite Hausdorff -measure on an -dimensional complex manifold and all the points of are nonremovable for a meromorphic mapping of into a compact Kähler manifold, then is a pure -dimensional complex analytic subset of
On nonimbeddability of Hartogs figures into complex manifolds
5 pagesWe propose a method to construct examples of strange imbeddings of Hartogs figures into complex manifolds. It gives an imbedding of a "thin" Hartogs figure which does not have any neighborhood biholomorphic to an open set in a Stein manifold, thus unswering a question of E. Poletsky. Then we give an example of a foliated manifold which does not admit any nontrivial imbeddings of a "thick" (i.e. usual) Hartogs figure, giving thus a counterexample to some "selfevident" statements used in foliation theory
Tameness of complex dimension in a real analytic set
Given a real analytic set X in a complex manifold and a positive integer d,
denote by A(d) the set of points p in X at which there exists a germ of a
complex analytic set of dimension d contained in X. It is proved that A(d) is a
closed semianalytic subset of X.Comment: Published versio
Functions holomorphic along holomorphic vector fields
The main result of the paper is the following generalization of Forelli's
theorem: Suppose F is a holomorphic vector field with singular point at p, such
that F is linearizable at p and the matrix is diagonalizable with the
eigenvalues whose ratios are positive reals. Then any function that has
an asymptotic Taylor expansion at p and is holomorphic along the complex
integral curves of F is holomorphic in a neighborhood of p.
We also present an example to show that the requirement for ratios of the
eigenvalues to be positive reals is necessary
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