Local Boundedness of Catlin q-Type

Date

2022-02-01

Author

Yazıcı, Özcan

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

217
views

0
downloads

In D'Angelo (Ann Math 115:615-637, 1982) introduced the notion of finite type for points p of a real hypersurface M of C-n by defining the order of contact Delta(q)(M, p) of complex-analytic q-dimensional varieties with M at p. Later, Catlin (Ann Math 126(1):131-191, 1987) defined q-type, D-q(M, p) for points of hypersurfaces by considering generic (n - q + 1)-dimensional complex aline subspaces of C-n. We define a generalization of the Catlin's q-type for an arbitrary subset M of C-n in a similar way that D'Angelo's 1-type, (M, p), is generalized in Lamel and Mir (Adv Math 335:696-734, 2018). Using recent results connecting the D'Angelo and Catlin q-types in Brinzanescu and Nicoara (Relating Catlin and D'Angelo q-types. arXiv:1707.08294, 2021) and building on D'Angelo's work on the openness of the set of points of finite Delta(q)-type, we prove the openness of the set of points of finite Catlin q-type for an arbitrary subset M subset of C-n.

Subject Keywords

Catlin type, order of contact, germs of holomorphic functions, subelliptic estimates, NEUMANN PROBLEM, ORDERS

URI

https://hdl.handle.net/11511/95318

Journal

MEDITERRANEAN JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.1007/s00009-021-01945-9

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Series solution of the wave equation in optic fiber Çıldır, Sema; Çakır, Serhat; Department of Physics (2007) In this study, the mapped Galerkin method was applied to solve the vector wave equation based on H field and to obtain the propagation constant in x y space. The vector wave equation was solved by the transformation of the infinite x y plane onto a unit square. Two-dimensional Fourier series expansions were used in the solutions. Modal fields and propagation constants of dielectric waveguides were calculated. In the first part of the study, all of the calculations were made in step index fibers. Transvers...
Geometric measures of entanglement UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01) The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01) Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2 Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28) We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphis...
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.

Citation Formats

Ö. Yazıcı, “Local Boundedness of Catlin q-Type,” MEDITERRANEAN JOURNAL OF MATHEMATICS, vol. 19, no. 1, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/95318.