Title :

Pollicott-Ruelle spectrum and Witten Laplacians

Author(s) :

Dang, Nguyen Viet [Auteur]
Probabilités, statistique, physique mathématique [PSPM]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of the European Mathematical Society

Publisher :

European Mathematical Society

Publication date :

2019

ISSN :

1435-9855

English keyword(s) :

microlocal analysis
resonances
Morse-Smale gradient flows
hyperbolic dynamical systems
differential topology

HAL domain(s) :

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]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Comment :

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

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL