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arXiv · 2505.01889

Global hypoellipticity for involutive systems on non-compact manifolds

Sandro Coriasco·Alexandre Kirilov·Wagner Augusto Almeida de Moraes·Pedro Meyer Tokoro
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Abstract

We study the global hypoellipticity of the operator $\mathbb{L} = \mathrm{d}_t + \sum_{k=1}^m ω_k \wedge \partial_{x_k}$, defined on differential forms over product manifolds of the form $M \times \mathbb{T}^m$, where $M$ is a non-compact manifold homeomorphic to the interior of a compact manifold with boundary, equipped with a scattering metric, and $ω_1,\dots,ω_m$ are smooth closed 1-forms on $M$. Extending previous results obtained in the compact setting, we characterize global hypoellipticity of $\mathbb{L}$ in terms of arithmetic properties of the forms $ω_k$. The analysis relies on microlocal techniques adapted to the scattering setting and a version of the Hodge Theorem for scattering manifolds.

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Sandro Coriasco, Alexandre Kirilov, Wagner Augusto Almeida de Moraes, Pedro Meyer Tokoro. 2025-05-03. Global hypoellipticity for involutive systems on non-compact manifolds. https://doi.org/10.1007/s12220-025-02267-y

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