An $L^2$-$\partial\overline\partial$-Lemma on a class of complete Kähler manifolds
Abstract
We prove an $L^2$-$\partial\overline\partial$-Lemma involving smooth square integrable forms on complete Kähler manifolds, provided that the unique self-adjoint extension of the Hodge Laplacian on the Hilbert space of $L^2$-forms has a gap in its spectrum near zero. This generalises the classical $\partial\overline\partial$-Lemma on compact Kähler manifolds.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint