On the Sobolev boundedness of vector fields on compact Riemannian manifolds

Duván Cardona; Alexandre Kirilov; Wagner A. A. de Moraes; André Pedroso Kowacs

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arXiv · 2404.00182

On the Sobolev boundedness of vector fields on compact Riemannian manifolds

Duván Cardona·Alexandre Kirilov·Wagner A. A. de Moraes·André Pedroso Kowacs

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Abstract

We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of eigenvalues associated with these vector fields. As an application, we demonstrate the ill-posedness of a class of Cauchy problems involving left-invariant vector fields on compact Lie groups.

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Duván Cardona, Alexandre Kirilov, Wagner A. A. de Moraes, André Pedroso Kowacs. 2024-03-29. On the Sobolev boundedness of vector fields on compact Riemannian manifolds. https://arxiv.org/abs/2404.00182

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