• Corpus ID: 239009544

# 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}
}```
• Published 14 October 2021
• Mathematics
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
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## References

SHOWING 1-8 OF 8 REFERENCES
Rigidity of Proper Holomorphic Maps Among Generalized Balls with Levi-Degenerate Boundaries
• Mathematics
• 2021
In this paper we studied a broader type of generalized balls which are domains on the complex projective with possibly Levi-degenerate boundaries. We proved rigidity theorems for proper holomorphic
A new gap phenomenon for proper holomorphic mappings from B^n into B^N
In this paper (Math. Res. Lett. 13 (2006). No 4, 509-523), the authors established a pseudo-normal form for proper holomoprhic mappings between balls in complex spaces with degenerate rank. This then
Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics
• Mathematics
• 2014
Using Green’s hyperplane restriction theorem, we prove that the rank of a Hermitian form on the space of holomorphic polynomials is bounded by a constant depending only on the maximum rank of the
Recent Progress on Two Problems in Several Complex Variables
• Mathematics
• 2007
We discuss the recent progress on two problems in Several Complex Variables. The first one is on the gap phenomenon for proper holomorphic maps between balls. The second one is on the precise
Some Properties of Enumeration in the Theory of Modular Systems
The object of this note is to discover the limiting relations which must •exist between the terms of the series Do, Dv ..., A, ••• where A is the number of linearly independent homogeneous
On the third gap for proper holomorphic maps between balls
• Mathematics
• 2012
Let \$\$F\$\$F be a proper rational map from the complex ball \$\$\mathbb B ^n\$\$Bn into \$\$\mathbb B ^N\$\$BN with \$\$n>7\$\$n>7 and \$\$3n+1 \le N\le 4n-7\$\$3n+1≤N≤4n-7. Then \$\$F\$\$F is equivalent to a map \$\$(G, 0,