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- W3105095029 abstract "On a class of asymptotically conical manifolds, we prove two types of low frequency estimates for the resolvent of the Laplace-Beltrami operator. The first result is a uniform $ L^2 rightarrow L^2 $ bound for $ langle r rangle^{-1} (- Delta_G - z)^{-1} langle r rangle^{-1} $ when $ mbox{Re}(z) $ is small, with the optimal weight $ langle r rangle^{-1} $. The second one is about powers of the resolvent. For any integer $N$, we prove uniform $ L^2 rightarrow L^2 $ bounds for $ langle epsilon r rangle^{-N} (-epsilon^{-2} Delta_G - Z)^{-N} langle epsilon r rangle^{-N} $ when $ mbox{Re}(Z) $ belongs to a compact subset of $ (0,+infty) $ and $ 0 < epsilon ll 1 $. These results are obtained by proving similar estimates on a pure cone with a long range perturbation of the metric at infinity." @default.
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- W3105095029 date "2015-01-15" @default.
- W3105095029 modified "2023-10-16" @default.
- W3105095029 title "Sharp Low Frequency Resolvent Estimates on Asymptotically Conical Manifolds" @default.
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- W3105095029 doi "https://doi.org/10.1007/s00220-014-2286-4" @default.
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