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This article follows the previous works [HKN] by Helffer-Klein-Nier and [HeNi1] by Helffer-Nier about the metastability in reversible diffusion processes via a Witten complex approach. Again, exponentially small eigenvalues of some self-adjoint realization of ∆ (0) f,h = −h 2 ∆ + |∇f (x)| 2 − h∆f (x) , are considered as the small parameter h > 0 goes to 0.… (More)
WKB p-forms are constructed as approximate solutions to boundary value problems associated with semi-classical Witten Laplacians. Naturally distorted Neumann or Dirichlet boundary conditions are considered.
Small eigenvalues of the Witten Laplacian acting on p-forms on a surface Abstract In this article, we are interested in the exponentially small eigenval-ues of the self adjoint realization of the semiclassical Witten Laplacian ∆ (p) f,h , in the general framework of p-forms, on a connected compact Riemannian manifold without boundary. Our purpose is to… (More)
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