A parametric version of Forstnerič’s splitting lemma. (English) Zbl 1435.32019
This paper gives a parametric version of Forstnerič’s splitting lemma in the special case of Euclidean space \(\mathbb{C}^n\) and compact parametric space. Following Forstnerič’s original method, the author constructs solution operators to \(\overline{\partial}\) that depend continuously on the domain and satisfy sup-norm estimates which depend continuously on the domain as well. Then the author is able to show the additive splitting, and hence the parametric version of Forstnerič’s result. It should be pointed out that the method using properties of the \(\overline{\partial}\)-operator can be generalized to other systems of linear partial differential equations admitting solution operators, or even to certain linear operators on presheaves.
Reviewer: Liwei Chen (Columbus)
MSC:
| 32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
| 32W05 | \(\overline\partial\) and \(\overline\partial\)-Neumann operators |
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