2002/06/15 by Peter Ebenfelt, Ebenfelt, Peter, Xiaojun Huang +3
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #math.DG
paper · pdf · doi:10.48550/arxiv.math/0206152
arxiv created 2002/06/15 · openalex publication_date 2002/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider local CR-immersions of a strictly pseudoconvex real hypersurface M⊂\bCn+1, near a point p∈ M, into the unit sphere \mathbb S⊂\bCn+d+1 with d>0. Our main result is that if there is such an immersion f\colon (M,p)→ \mathbb S and d < n/2, then f is \em rigid in the sense that any other immersion of (M,p) into \mathbb S is of the form ϕ∘ f, where ϕ is a biholomorphic automorphism of the unit ball \mathbb B⊂\bCn+d+1. As an application of this result, we show that an isolated singularity of an irreducible analytic variety of codimension d in \bCn+d+1 is uniquely determined up to affine linear transformations by the local CR geometry at a point of its Milnor link.