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Parametrix Construction and Invertibility of $Δ_g + 1$
Given a manifold $M$ with an asymptotically cylindrical end, we construct the parametrix for the shifted Laplace operator $Δ_g + 1$ on the blown-up $b$-double space $M_b^2$. We will review the geometry of manifold with a cylindrical end and construct the inverse directly via separation of variables,
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