# A hyperplane restriction theorem for holomorphic mappings and its application for the gap conjecture

@inproceedings{Gao2021AHR, title={A hyperplane restriction theorem for holomorphic mappings and its application for the gap conjecture}, author={Yung Gao and Sui-chung. Ng}, year={2021} }

We established a hyperplane restriction theorem for the local holomorphic mappings between projective spaces, which is inspired by the corresponding theorem of Green for OPn(d). Our theorem allows us to give the first proof for the existence of gaps (albeit smaller) at all levels for the rational proper maps between complex unit balls, conjectured by Huang-Ji-Yin. In addition, our proof does not distinguish the unit balls from other generalized balls and thus it simultaneously demonstrates the…

## 3 Citations

Local orthogonal maps and rigidity of holomorphic mappings between real hyperquadrics

- Mathematics
- 2021

We introduced a new coordinate-free approach to study the Cauchy-Riemann (CR) maps between the real hyperquadrics in the complex projective space. The central theme is based on a notion of…

On the rank of Hermitian polynomials and the SOS Conjecture

- Mathematics
- 2021

Let z ∈ C and ‖z‖ be its Euclidean norm. Ebenfelt proposed a conjecture regarding the possible ranks of the Hermitian polynomials in z, z̄ of the form A(z, z̄)‖z‖2, known as the SOS Conjecture, where…

Orthogonal pair and a rigidity problem for Segre maps between hyperquadrics

- Mathematics
- 2021

Being motivated by the orthogonal maps studied in [GN1], orthogonal pairs between the projective spaces equipped with possibly degenerate Hermitian forms were introduced. In addition, orthogonal…

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