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Below I have given what I am calling as the ${\rm Witten{-}Laplacian}_{s,p}$ on a Riemannian manifold $(M,g)$ for any constant $s >0$ and $p \in C^2(M,g)$ How generally is it true that this ${\rm ...

It is well known that compact Riemannian manifolds $(M, g)$ with periodic geodesic flows have ( Besse Book) exceptional spectral properties: the spectrum of $ \sqrt{ - \Delta}$, the square root of ...