We study the global hypoellipticity of an operator L defined on differential forms over product manifolds of the form M × T^m , where M is a non-compact manifold, given by the interior of a scattering manifold, and T^m is the m-dimensional torus. Extending previous results obtained in the compact setting, we characterize the global hypoellipticity of L. The analysis relies on microlocal techniques, adapted to the scattering setting, and a version of the Hodge Theorem for scattering manifolds.
Global Hypoellipticity for Involutive Systems on Non-Compact Manifolds
Coriasco Sandro;Kirilov A.;Tokoro Pedro meyer
2026-01-01
Abstract
We study the global hypoellipticity of an operator L defined on differential forms over product manifolds of the form M × T^m , where M is a non-compact manifold, given by the interior of a scattering manifold, and T^m is the m-dimensional torus. Extending previous results obtained in the compact setting, we characterize the global hypoellipticity of L. 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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