ABSTRACT
In this paper, we prove the existence of (global) solutions of the Poincaré-Lelong equation , where f is a d-closed
form and is in the weighted Hilbert space with Gaussian measure, i.e.
. The novelty of this paper is to apply a weighted
version of the Poincaré Lemma for 2-forms and then apply Hörmander's
solutions for Cauchy–Riemann equations. In both cases, the same weight
is used.
Acknowledgements
The research of the second named author is in part supported by a grant from 2019 Pippert Science Research Scholar at Purdue University Fort Wayne. He is thankful for the Pippert family's generosity and continuing support for science research.
Disclosure statement
No potential conflict of interest was reported by the author(s).