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Creators/Authors contains: "Zhu, Weixia"

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  1. ; (, Mathematische Annalen)
    Abstract We study holomorphic mapsFfrom a smooth Levi non-degenerate real hypersurface$$ M_{\ell }\subset {\mathbb {C}}^n $$ M ℓ ⊂ C n into a hyperquadric$$ {\mathbb {H}}_{\ell '}^N $$ H ℓ ′ N with signatures$$ \ell \le (n-1)/2 $$ ℓ ≤ ( n - 1 ) / 2 and$$ \ell '\le (N-1)/2,$$ ℓ ′ ≤ ( N - 1 ) / 2 , respectively. Assuming that$$ N - n < n - 1,$$ N - n < n - 1 , we prove that if$$ \ell = \ell ',$$ ℓ = ℓ ′ , thenFis either CR transversal to$$ {\mathbb {H}}_{\ell }^N $$ H ℓ N at every point of$$ M_{\ell },$$ M ℓ , or it maps a neighborhood of$$ M_{\ell } $$ M ℓ in$$ {\mathbb {C}}^n $$ C n into$$ {\mathbb {H}}_{\ell }^N.$$ H ℓ N . Furthermore, in the case where$$ \ell ' > \ell ,$$ ℓ ′ > ℓ , we show that ifFis not CR transversal at$$0\in M_\ell ,$$ 0 ∈ M ℓ , then it must be transversally flat. The latter is best possible. 
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  2. ; ; (, Journal of Mathematical Analysis and Applications)
    Full Text Available 
  3. ; (, The Journal of Geometric Analysis)
    Abstract We study spectral stability of the$${\bar{\partial }}$$ ∂ ¯ -Neumann Laplacian on a bounded domain in$${\mathbb {C}}^n$$ C n when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues of the$${\bar{\partial }}$$ ∂ ¯ -Neumann Laplacian on bounded pseudoconvex domains in$${\mathbb {C}}^n$$ C n , lower semi-continuity properties on pseudoconvex domains that satisfy property (P), and quantitative estimates on smooth bounded pseudoconvex domains of finite D’Angelo type in$${\mathbb {C}}^n$$ C n . 
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