1. Full name:     Nguyen Thi Lan Huong              2. Sex: Female

3. Date of birth: 29/12/1979                                4. Place of birth: Thai Nguyen

5. Admission decision number: 2556/QĐ-ĐHKHTN (26/7/2017).

6. Changes in academic process: 318/QĐ-ĐHKHTN (01/02/2021); 231/QĐ-ĐHKHTN (27/01/2022); 72/QĐ-ĐHKHTNHN (10/01/2023).

7. Official thesis title: The automorphism group of some domains in Cn and the boundary behaviour of the squeezing function.

8. Major: Analysis                                                          9. Code: 62 46 01 02

10. Supervisors: Ninh Van Thu

11. Summary of the new findings of the thesis

1) Describe the automorphic group of the finite type model in Cn defined by: Mp = {z ∈ Cn : Re(zn) + P(z ′ ) < 0}, where P is a weighted subharmonic polynomial on Cn-1 and does not contain a harmonic element.

2) Prove that if the squeezing function tends to 1 at the orbital boundary point ξ0 ∈ ∂Ω with a smooth, pseudo-convex ∂Ω, has a finite D'Angelo type and has at most an argument of the Levi form equal to 1 at ξ0, then ξ0 is a pseudo-convex boundary point.

3) Prove that if the squeezing function tends to 1 at the orbital boundary point ξ0 ∈ ∂Ω with a smooth, linear convex ∂Ω, of finite D'Angelo type at ξ0, then ξ0 is pseudo-convex.

4) Give a subestimate for the squeezing function for the generalized Ellipsoid domain.

12. Paratical applicability, if any:

The research results of the thesis have the ability to apply to practical problems of Multivariate Complex Calculus.

13. Further research directions, if any

Describes the automorphism group of the domain in Cn and describes the boundary shape of the squeezing function of the finite type domain in Cn.

14. Thesis-related publications:

[1] On the automophism Groups of Finite Multitype models in Cn, The journal of Geometric Analysis, January 2019, Volume 29, Issue 1, pp 428–450.

[2] A note on the boundary behaviour of the squeezing function and Fridman invariant, Bulletin of the Korean Mathematical Society, 5/9/2020, Volume 57, Issue 5, pp 1241–1249.

[3] Conference report "On the automorphism group of finite multitype model in Cn", Calculus and Geometry Summer School, University of Education - University of Da Nang, 11-14/06/2020.

[4] Conference report "A note on the boundary behaviour of the squeezing function and Fridman invariant", Conference "Some topics in mathematics and applications", University of Science and Technology - Hanoi National University, 30-31/10/2021.