Pollicott-Ruelle spectrum and Witten Laplacians
Type de document :
Article dans une revue scientifique: Article original
DOI :
URL permanente :
Titre :
Pollicott-Ruelle spectrum and Witten Laplacians
Auteur(s) :
Dang, Nguyen Viet [Auteur]
Probabilités, statistique, physique mathématique [PSPM]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Probabilités, statistique, physique mathématique [PSPM]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Titre de la revue :
Journal of the European Mathematical Society
Éditeur :
European Mathematical Society
Date de publication :
2019
ISSN :
1435-9855
Mot(s)-clé(s) en anglais :
microlocal analysis
resonances
Morse-Smale gradient flows
hyperbolic dynamical systems
differential topology
resonances
Morse-Smale gradient flows
hyperbolic dynamical systems
differential topology
Discipline(s) HAL :
Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Théorie spectrale [math.SP]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Théorie spectrale [math.SP]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Résumé en anglais : [en]
We study the asymptotic behaviour of eigenvalues and eigenmodes of the Witten Laplacian on a smooth compact Riemannian manifold without boundary. We show that they converge to the Pollicott-Ruelle spectrum of the corresponding ...
Lire la suite >We study the asymptotic behaviour of eigenvalues and eigenmodes of the Witten Laplacian on a smooth compact Riemannian manifold without boundary. We show that they converge to the Pollicott-Ruelle spectrum of the corresponding gradient flow acting on appropriate anisotropic Sobolev spaces. In particular, our results relate the approach of Laudenbach and Harvey–Lawson to Morse theory using currents, which was discussed in previous work of the authors, and Witten's point of view based on semiclassical analysis and tunneling. As an application of our methods, we also construct a natural family of quasimodes satisfying the Witten-Helffer-Sjöstrand tunneling formulas and the Fukaya conjecture on Witten deformation of the wedge product.Lire moins >
Lire la suite >We study the asymptotic behaviour of eigenvalues and eigenmodes of the Witten Laplacian on a smooth compact Riemannian manifold without boundary. We show that they converge to the Pollicott-Ruelle spectrum of the corresponding gradient flow acting on appropriate anisotropic Sobolev spaces. In particular, our results relate the approach of Laudenbach and Harvey–Lawson to Morse theory using currents, which was discussed in previous work of the authors, and Witten's point of view based on semiclassical analysis and tunneling. As an application of our methods, we also construct a natural family of quasimodes satisfying the Witten-Helffer-Sjöstrand tunneling formulas and the Fukaya conjecture on Witten deformation of the wedge product.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Commentaire :
Revised version following referees suggestions. To appear J. Eur. Math. Soc.
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Source :
Date de dépôt :
2025-01-24T17:10:44Z
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- DaRi-Witten-revised-april-2019.pdf
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