On the Sobolev boundedness of vector fields on compact Riemannian manifolds

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

On the Sobolev boundedness of vector fields on compact Riemannian manifolds

Analysis of PDEs 2025-06-23 v2

Authors: Duván Cardona , Alexandre Kirilov , Wagner A. A. de Moraes , André Pedroso Kowacs

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.

Keywords

Sobolev boundedness left-invariant vector fields compact Riemannian manifolds pseudo-differential operators eigenvalue asymptotics ill-posed Cauchy problem

Cite

@article{arxiv.2404.00182,
  title  = {On the Sobolev boundedness of vector fields on compact Riemannian manifolds},
  author = {Duván Cardona and Alexandre Kirilov and Wagner A. A. de Moraes and André Pedroso Kowacs},
  journal= {arXiv preprint arXiv:2404.00182},
  year   = {2025}
}

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10 Pages

On the Sobolev boundedness of vector fields on compact Riemannian manifolds

Abstract

Keywords

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