# The linearity of proper holomorphic maps between balls in the low codimension case

@article{Faran1986TheLO,
title={The linearity of proper holomorphic maps between balls in the low codimension case},
author={James J. Faran},
journal={Journal of Differential Geometry},
year={1986},
volume={24},
pages={15-17}
}
• J. Faran
• Published 1986
• Mathematics
• Journal of Differential Geometry
Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications
• D. Son
• Mathematics
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
• 2021
We study the geometry of the second fundamental form of the semi-isometric CR immersions from strictly pseudoconvex CR manifolds into Kahler manifolds in connection with several problems in complex
Holomorphic mappings between pseudoellipsoids in different dimensions
• Mathematics
• 2014
We give a necessary and sufficient condition for the existence of nondegenerate holomorphic mappings between pseudoellipsoidal real hypersurfaces, and provide an explicit parametrization for the
Spherical CR Geometry and Holomorphically Immersed Spheres
We survey some related recent progress in proper holomorphic mappings between balls and CR maps between spheres. 2000 Mathematics Subject Classification: 32H02, 32Q45, 30F45, 51M10.
Constructing Group-Invariant CR Mappings
• Mathematics
• 2022
We construct CR mappings between spheres that are invariant under actions of finite unitary groups. In particular, we combine a tensoring procedure with D’Angelo’s construction of a canonical
A hyperplane restriction theorem for holomorphic mappings and its application for the gap conjecture
• Mathematics
• 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
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 CR maps from the sphere into the tube over the future light cone
• Mathematics
• 2021
We determine all local smooth or formal CR maps from the unit sphere S ⊂ C into the tube T := C × iR ⊂ C over the future light cone C := { x ∈ R : x 1 + x 2 = x 3 , x3 > 0 } . This result leads to a
Orthogonal pair and a rigidity problem for Segre maps between hyperquadrics
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
Sum of squares conjecture: the monomial case in $$\mathbb {C}^3$$
• Mathematics
• 2021
The goal of this article is to prove the Sum of Squares Conjecture for real polynomials $$r(z,\bar{z})$$ on $$\mathbb {C}^3$$ with diagonal coefficient matrix. This conjecture describes the