Top-Degree Global Solvability for Tube Complexes in Gevrey Ultradistributions
Abstract
Let s>1, let M be a connected, non-compact, oriented real-analytic manifold, and let ω1,…,ωm be real-valued closed $1$-forms of Gevrey order s on M. We study the differential complex naturally associated with this family on M×𝕋m. We prove that its top-degree operator is globally solvable in Roumieu Gevrey ultradistributions, or equivalently that the corresponding top-degree cohomology vanishes. No global hypoellipticity assumption and no arithmetic condition on the periods of the defining forms are required. The proof is carried out in the physical variables and combines fiber translations, a local normal form, and a transport formula along paths in the base manifold. These tools yield propagation of Gevrey regularity, non-confinement of Gevrey singularities, and the support control needed to apply an abstract solvability criterion. The result highlights a sharp contrast with the compact setting, where compatibility conditions are unavoidable and solvability for compatible data may depend on exponential small-denominator conditions.
Versions
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BibTeX
@misc{coriasco2026topdegree,
title = {{Top-Degree Global Solvability for Tube Complexes in Gevrey Ultradistributions}},
author = {Sandro Coriasco and Alexandre Kirilov and Wagner Augusto Almeida de Moraes and Pedro Meyer Tokoro},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.28923},
eprint = {2607.28923},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28923},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Top-Degree Global Solvability for Tube Complexes in Gevrey Ultradistributions
AU - Sandro Coriasco
AU - Alexandre Kirilov
AU - Wagner Augusto Almeida de Moraes
AU - Pedro Meyer Tokoro
PY - 2026
DA - 2026/07/31
PB - arXiv
DO - 10.48550/arxiv.2607.28923
UR - https://arxiv.org/abs/2607.28923
AB - Let s>1, let M be a connected, non-compact, oriented real-analytic manifold, and let ω_1,…,ω_m be real-valued closed $1$-forms of Gevrey order s on M. We study the differential complex naturally associated with this family on M×𝕋^m. We prove that its top-degree operator is globally solvable in Roumieu Gevrey ultradistributions, or equivalently that the corresponding top-degree cohomology vanishes. No global hypoellipticity assumption and no arithmetic condition on the periods of the defining forms are required. The proof is carried out in the physical variables and combines fiber translations, a local normal form, and a transport formula along paths in the base manifold. These tools yield propagation of Gevrey regularity, non-confinement of Gevrey singularities, and the support control needed to apply an abstract solvability criterion. The result highlights a sharp contrast with the compact setting, where compatibility conditions are unavoidable and solvability for compatible data may depend on exponential small-denominator conditions.
ER -