About small eigenvalues of Witten Laplacian

Abstract

We study the eigenvalues of the semiclassical Witten Laplacian ${\Delta }_{\varphi }$ associated to a potential $\varphi$. We consider the case where the sequence of Arrhenius numbers $S_1\le \dots \le S_n$ associated to $\varphi$ is degenerated, that is the preceding inequality are not necessarily strict.

58 pages, 10 figures

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