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• W2023276308 abstract "In this paper, we study the asymptotic behavior of solutions to Schrödinger equations on manifolds with nonnegative Ricci curvature and Euclidean volume growth. As a first application, we get a sharp asymptotic estimate on the Green's function for the Laplacian which sharpens results of Li and Yau. Next we establish a definite gap in the possible rates of decay of exterior harmonic functions on these manifolds. When the manifold also has quadratic curvature decay, we get supremum estimates on the C2 norm of the Green's function; this has function theoretic implications for these manifolds. We then give a generalization to manifolds with nonnegative Ricci curvature outside a compact set. Finally, we study Schrödinger operators where the potential decays quadratically at infinity. In this setting, we obtain a geometric version at infinity of a classical theorem of Bers." @default.
• W2023276308 created "2016-06-24" @default.
• W2023276308 creator A5014724625 @default.
• W2023276308 creator A5070168028 @default.
• W2023276308 date "1997-01-01" @default.
• W2023276308 modified "2023-10-16" @default.
• W2023276308 title "Large scale behavior of kernels of Schrodinger operators" @default.
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• W2023276308 doi "https://doi.org/10.1353/ajm.1997.0037" @default.
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