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The Kobayashi metric in the normal direction and the mapping problem
Siqi Fu
Estimates of the Kobayashi metric in the normal direction are used to study the mapping problem in several complex variables.
The -cohomology groups, holomorphic Morse inequalities, and finite type conditions
Siqi Fu, Howard Jacobowitz
We study spectral behavior of the complex Laplacian on forms with values in the tensor power of a holomorphic line bundle over a smoothly bounded domain with degene…
Spectrum of the d-bar-Neumann Laplacian on polydiscs
Siqi Fu
The spectrum of the d-bar-Neumann Laplacian on a polydisc in several complex variables is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, s…
Hearing the type of a domain in C^2 with the d-bar-Neumann Laplacian
Siqi Fu
A smooth bounded pseudoconvex domain in two complex variables is of finite type if and only if the number of eigenvalues of the d-bar-Neumann Laplacian that are less than or equal…
Hearing pseudoconvexity with the Kohn Laplacian
Siqi Fu
A bounded domain in several complex variables with connected Lipschitz boundary is pseudoconvex if and only if the bottom of the (essential) spectrum of the Kohn Laplacian is posit…
Compactness in the d-bar Neumann problem, magnetic Schrodinger operators, and the Aharonov-Bohm effect
Michael Christ, Siqi Fu
Compactness of the d-bar Neumann operator is studied for weakly pseudoconvex bounded Hartogs domains in two dimensions. A nonsmooth example is constructed in which condition (P) fa…