Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds

We study the spectral theory and the resolvent of the vector field generating the frame flow of closed hyperbolic three-dimensional manifolds on some family of anisotropic Sobolev spaces. We show the existence of a spectral gap and prove resolvent estimates using semiclassical methods.

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Bibliographische Detailangaben
Veröffentlicht in:	Annales Henri Poincaré 2021-11, Vol.22 (11), p.3565-3617
Hauptverfasser:	Guillarmou, Colin, Küster, Benjamin
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical and Quantum Gravitation Differential Geometry Dynamical Systems Dynamical Systems and Ergodic Theory Elementary Particles Fields (mathematics) Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Sobolev space Spectra Spectral Theory Theoretical Three dimensional flow
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Beschreibung
Zusammenfassung:	We study the spectral theory and the resolvent of the vector field generating the frame flow of closed hyperbolic three-dimensional manifolds on some family of anisotropic Sobolev spaces. We show the existence of a spectral gap and prove resolvent estimates using semiclassical methods.
ISSN:	1424-0637 1424-0661
DOI:	10.1007/s00023-021-01068-7