Global Gevrey Hypoellipticity of Involutive Systems on Non-Compact Manifolds
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915804043280384 |
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| author | Coriasco, Sandro Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer |
| author_facet | Coriasco, Sandro Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer |
| contents | We investigate the global Gevrey hypoellipticity of a class of first-order differential operators associated with tube-type involutive structures on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold diffeomorphic to the interior of a compact manifold with boundary and $\mathbb{T}^m$ is the $m$-dimensional torus. For $s>1$, we work in Gevrey classes of Roumieu and Beurling type. A key step is the construction, on $M$, of a scattering metric whose coefficients are Gevrey of order $s$ in every analytic chart; this allows us to use Hodge theory and obtain Gevrey regularity for the harmonic forms. Under a natural condition on the defining closed $1$-forms, we obtain a sharp criterion for global Gevrey hypoellipticity in terms of rationality and (Roumieu/Beurling) exponential Liouville behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16366 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Gevrey Hypoellipticity of Involutive Systems on Non-Compact Manifolds Coriasco, Sandro Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer Analysis of PDEs Primary 35N10, 58J10, Secondary 35B65, 58J40 We investigate the global Gevrey hypoellipticity of a class of first-order differential operators associated with tube-type involutive structures on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold diffeomorphic to the interior of a compact manifold with boundary and $\mathbb{T}^m$ is the $m$-dimensional torus. For $s>1$, we work in Gevrey classes of Roumieu and Beurling type. A key step is the construction, on $M$, of a scattering metric whose coefficients are Gevrey of order $s$ in every analytic chart; this allows us to use Hodge theory and obtain Gevrey regularity for the harmonic forms. Under a natural condition on the defining closed $1$-forms, we obtain a sharp criterion for global Gevrey hypoellipticity in terms of rationality and (Roumieu/Beurling) exponential Liouville behavior. |
| title | Global Gevrey Hypoellipticity of Involutive Systems on Non-Compact Manifolds |
| topic | Analysis of PDEs Primary 35N10, 58J10, Secondary 35B65, 58J40 |
| url | https://arxiv.org/abs/2602.16366 |