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Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.

Francis Nier (2004)

Journées Équations aux dérivées partielles

We present here a simplified version of recent results obtained with B. Helffer and M. Klein. They are concerned with the exponentally small eigenvalues of the Witten Laplacian on 0 -forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of Δ f , h ( 0 ) and solves efficiently the question of weakly resonant wells.

Quaternionic contact structures in dimension 7

David Duchemin (2006)

Annales de l’institut Fourier

The conformal infinity of a quaternionic-Kähler metric on a 4 n -manifold with boundary is a codimension 3 distribution on the boundary called quaternionic contact. In dimensions 4 n - 1 greater than 7 , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7 , we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact structures...

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