$L^2$-estimates for the $d$-operator acting on super forms

Details $L^2$-estimates for the $d$-operator acting on super forms $L^2$-estimates for the $d$-operator acting on super forms

2011-09-19

arxiv.org/abs/1109.3983v1

Mathematics

Complex Variables

22 pages

Scientific paper

In the setting of super forms developed in a previous article by the author, we introduce the notion of $\mathbb{R}$-K\"ahler metrics on $\mathbb{R}^{n}$. We consider existence theorems and $L^{2}-$estimates for the equation $d\alpha=\beta$, where $\alpha$ and $\beta$ are super forms, in the spirit of H\"ormander's $L^{2}-$estimates for the $\bar{\partial}-$equation on a complex K\"ahler manifold.

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