An $L^2$-$\partial\overline\partial$-Lemma on a class of complete K\"ahler manifolds

Riccardo Piovani

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arXiv · 2602.08831

An $L^2$-$\partial\overline\partial$-Lemma on a class of complete K\"ahler manifolds

Riccardo Piovani

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Abstract

We prove an $L^2$-$\partial\overline\partial$-Lemma involving smooth square integrable forms on complete K\"ahler 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 K\"ahler manifolds.

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Riccardo Piovani. 2026-02-09. An $L^2$-$\partial\overline\partial$-Lemma on a class of complete K\"ahler manifolds. https://arxiv.org/abs/2602.08831

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