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Pré-Publication, Document De Travail Année : 2023

Asymptotic regularity of sub-Riemannian eigenfunctions in dimension 3: the periodic case

Gabriel Rivière

Résumé

On the unit tangent bundle of a compact Riemannian surface of constant nonzero curvature, we study semiclassical Schrödinger operators associated with the natural sub-Riemannian Laplacian built along the horizontal bundle. In that setup , the involved Reeb flow is periodic and we show that high-frequency Schrödinger eigenfunctions enjoy extra regularity properties. As an application, we derive regularity properties for low-energy eigenmodes of semiclassical magnetic Schrödinger operators on the underlying surface by considering joint eigenfunctions with the Reeb vector field.
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hal-04270813 , version 1 (05-11-2023)

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Gabriel Rivière. Asymptotic regularity of sub-Riemannian eigenfunctions in dimension 3: the periodic case. 2023. ⟨hal-04270813⟩
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