Global solvability and propagation of regularity of sums of squares on compact manifolds

2020/10/11 by Gabriel Araújo, Araújo, Gabriel, Igor A. Ferra +3 · 2 citations
Computer Science · Mathematics · #35A01 (primary) #35R01 #35R03 (secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2010.05364

openalex publication_date 2020/10/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We investigate global solvability, in the framework of smooth functions and Schwartz distributions, of certain sums of squares of vector fields defined on a product of compact Riemannian manifolds T × G, where G is further assumed to be a Lie group. As in a recent article due to the authors, our analysis is carried out in terms of a system of left-invariant vector fields on G naturally associated with the operator under study, a simpler object which nevertheless conveys enough information about the original operator so as to fully encode its solvability. As a welcome side effect of the tools developed for our main purpose, we easily prove a general result on propagation of regularity for such operators.

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• A Fourier analysis for (θ,T)-periodic functions and applications
• Global Solvability for Involutive Systems on Non-Compact Manifolds

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