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Small eigenvalues of the Witten Laplacian acting on p-forms on a surface

Dorian Le Peutrec 1

(08/03/2010)

In this article, we are interested in the exponentially small eigenvalues of the self adjoint realization of the semiclassical Witten Laplacian $\Delta_{f,h}^{(p)}$, in the general framework of p-forms, on a connected compact Riemannian manifold without boundary. Our purpose is to notice that the knowledge of (the asymptotic formulas for) the smallest non zero eigenvalues of the self adjoint realization of $\Delta_{f,h}^{(0)}$ (acting on functions), presented in [HeKlNi], essentially contains all the necessary information to the treatment of the case of oriented surfaces, for p-forms. The function f is assumed to be a Morse function on the manifold.

1 :	Institut für Angewandte Mathematik (IAM)
	Universität Bonn

Domaine

:

Mathématiques/Théorie spectrale

Mots Clés : Witten complex – exponentially small eigenvalues – differential p-forms on surfaces.

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Contributeur : Dorian Le Peutrec <>

Soumis le : Mercredi 14 Avril 2010, 12:34:38

Dernière modification le : Vendredi 16 Avril 2010, 19:58:00