Abstract:
We study the induced $\overline{\partial}\partial$-equation on a positive current in a complex manifold. We show that $L^2$-estimates are satisfied for $\overline{\partial}\partial$-equation on a positive closed current of bidegree (1, 1) on a pseudoconvex domain in $C^n$. We also discuss a currents of higher bidegree.
Keywords:$\overline{\partial}\partial$-equation, positive current, differention form, complex manifold, primitive form, definite quadratic forms, differention operators on current, existence theorems for $\overline{\partial}\partial$ on closed current, currents of higher bidegree.
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