Holomorphic extension of meromorphic mappings along real analytic hypersurfaces

Let M subset of C-n be a real analytic hypersurface, M' subset of C-N (N >= n) be a strongly pseudoconvex real algebraic hypersurface of the special form, and F be a meromorphic mapping in a neighborhood of a point p is an element of M which is holomorphic in one side of M. Assuming some additional conditions for the mapping F on the hypersurface M, we proved that F has a holomorphic extension to p. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensions.


Finite type points on subsets of C-n
Yazıcı, Özcan (Elsevier BV, 2020-07-01)
In [4], D'Angelo introduced the notion of points of finite type for a real hypersurface M subset of C-n and showed that the set of points of finite type in M is open. Later, Lamel-Mir [8] considered a natural extension of D'Angelo's definition for an arbitrary set M subset of C-n. Building on D'Angelo's work, we prove the openness of the set of points of finite type for any subset M subset of C-n.
Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes
Lefloch, Philippe G.; Okutmuştur, Baver; Neves, Wladimir (Springer Science and Business Media LLC, 2009-07-01)
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L (1)-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L (1) norm is of order h (1/4) at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theo...
On homology of real algebraic varieties
Ozan, Yıldıray (American Mathematical Society (AMS), 2001-01-01)
Let R be a commutative ring with unity and X an R-oriented compact nonsingular real algebraic variety of dimension n. If i : X --> X-C is any nonsingular complexification of X, then the kernel, which we will denote by KHk(X, R), of the induced homomorphism i(*) : H-k(X, R) --> H-k(X-C, R) is independent of the complexification. In this work, we study KHk(X, R) and give some of its applications.
Legendrian realization in convex Lefschetz fibrations and convex stabilizations
Akbulut, Selman; Arıkan, Mehmet Fırat (Walter de Gruyter GmbH, 2015-05-01)
We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induced) convex open book on partial derivative W, can be assumed to be Legendrian in partial derivative W with the induced contact structure. This can be thought as the extension of Giroux's Legendrian realization (which holds for contact open books) for the case of convex open books. We also s...
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications
Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
Citation Formats
Ö. Yazıcı, “Holomorphic extension of meromorphic mappings along real analytic hypersurfaces,” ANNALI DI MATEMATICA PURA ED APPLICATA, pp. 1337–1342, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35746.