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]

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

Discipline(s) HAL :

Mathematics [math]/Dynamical Systems [math.DS]
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 >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Commentaire :

Revised version following referees suggestions. To appear J. Eur. Math. Soc.

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL