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Local Boundedness of Catlin q-Type
Date
2022-02-01
Author
Yazıcı, Özcan
Metadata
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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
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BibTeX
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.