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This article follows the previous works [HKN] by Helffer-KleinNier 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 ∆ f,h = −h∆ + |∇f(x)| − h∆f(x) , are considered as the small parameter h > 0 goes to 0. The function… (More)

See inside back cover or pjm.math.berkeley.edu/apde for submission instructions. The subscription price for 2010 is US $120/year for the electronic version, and $180/year for print and electronic. Subscriptions, requests for back issues from the last three years and changes of subscribers address should be sent to Mathematical Sciences Publishers, published… (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. MSC 2000: 58J37 (58J10 58J32 81Q20)

- Dorian Le Peutrec
- Asymptotic Analysis
- 2011

In this article, we are interested in the exponentially small eigenvalues of the self adjoint realization of the semiclassical Witten Laplacian ∆ f,h, 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… (More)

In this paper, we derive from the supersymmetry of the Witten Laplacian Brascamp-Lieb’s type inequalities for general differential forms on compact Riemannian manifolds with boundary. In addition to the supersymmetry, our results essentially follow from suitable decompositions of the quadratic forms associated with the Neumann and Dirichlet self-adjoint… (More)

- Dorian Le Peutrec, Francis Nier, Claude Viterbo, Dorian Le Peutrec, C. Viterbo
- 2017

Accurate asymptotic expressions are given for the exponentially small eigenvalues of Witten Laplacians acting on p-forms. The key ingredient, which replaces explicit formulas for global quasimodes in the case p = 0, is Barannikov’s presentation of Morse theory in [Bar]. MSC2010: 57N65, 58J32, 58J37, 58J50, 81Q10, 81Q20

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