Top-Degree Global Solvability for Tube Complexes in Gevrey Ultradistributions

2026/07/31 by Sandro Coriasco, Alexandre Kirilov, Wagner Augusto Almeida de Moraes +1
Mathematics · #math.AP #msc:35A01 #msc:46F05 #msc:35R01 #msc:58J10

paper · pdf

20 pages

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

Let s>1, let M be a connected, non-compact, oriented real-analytic manifold, and let ω₁,…,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×\mathbbT^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.

Citations

• Global hypoellipticity for involutive systems on non-compact manifolds
• Global solvability and cohomology of tube structures on compact manifolds
• Regularity and solvability of linear differential operators in Gevrey spaces: omitted proofs