$L^2$-estimates for the $d$-operator acting on super forms
Abstract
In the setting of super forms developed in a previous article by the author, we introduce the notion of $\mathbb{R}$-Kähler 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 Hörmander's $L^{2}-$estimates for the $\bar{\partial}-$equation on a complex Kähler manifold.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2011
- DOI:
- 10.48550/arXiv.1109.3983
- arXiv:
- arXiv:1109.3983
- Bibcode:
- 2011arXiv1109.3983L
- Keywords:
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- Mathematics - Complex Variables;
- Mathematics - Functional Analysis
- E-Print:
- 22 pages