Finite type points on subsets of Cn

The research article “Finite type points on subsets of Cⁿ”, authored by METU member Asst. Prof. Özcan Yazıcı, has been published in Journal of Mathematical Analysis and Applications.

In [4], D'Angelo introduced the notion of points of finite type for a real hypersurface M⊂Cⁿ 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⊂Cⁿ. Building on D'Angelo's work, we prove the openness of the set of points of finite type for any subset M⊂Cn.

Yazici, O. (2020). Finite type points on subsets of cn. Journal of Mathematical Analysis and Applications, 487(1) doi:10.1016/j.jmaa.2020.123978

Article access: https://www.sciencedirect.com/science/article/pii/S0022247X20301402?via%3Dihub

Keywords:

Finite type; Germs of holomorphic functions; Order of contact