Asymptotic estimate of a twisted Cauchy-Riemann operator with Neumann boundary condition

Abstract

For a holomorphic function f defined on a strongly pseudo-convex domain in {ℂ}^n such that it has only isolated critical points, we define a twisted Cauchy-Riemann operator {{\displaystyle \bar{\partial }}}_{\tau f}:\bar{\partial }+\tau \partial f\wedge. We will give an asymptotic estimate of the corresponding harmonic forms as τ tends to infinity. This asymptotic estimate is used to recover the residue pairing of the singularity defined by f.

Keywords

Asymptotic estimate / residue pairing

References

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Higher Education Press and Springer-Verlag GmbH Germany