In this paper we consider the Witten Laplacian on 0-forms and give sufficient conditions under which the Witten Laplacian admits a compact resolvent. These conditions are imposed on the potential itself, involving the control of high order derivatives by lower ones, as well as the control of the positive eigenvalues of the Hessian matrix. This compactness criterion for resolvent is inspired by the one for the Fokker-Planck operator. Our method relies on the nilpotent group techniques developed by Helffer-Nourrigat [Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, 1985]
Compactness of the resolvent for the Witten Laplacian
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Nom de l'orateur
Wei-Xi Li
Etablissement de l'orateur
Wuhan University, School of Mathematics and Statistics
Date et heure de l'exposé
Lieu de l'exposé
Salle des séminaires