Given a complete Riemannian manifold M and a smooth positive function w on M, let L = - Δ - ∇(log w) acting on L2(M, w dV). Generalizing techniques used in the case of the Laplacian, we obtain upper and lower bounds for the first non-zero eigenvalue of L, for M compact, and for the bottom of the spectrum, for M non-compact.
Eigenvalue estimates for the weighted laplacian on a Riemannian manifold
SETTI, ALBERTO GIULIO
1998-01-01
Abstract
Given a complete Riemannian manifold M and a smooth positive function w on M, let L = - Δ - ∇(log w) acting on L2(M, w dV). Generalizing techniques used in the case of the Laplacian, we obtain upper and lower bounds for the first non-zero eigenvalue of L, for M compact, and for the bottom of the spectrum, for M non-compact.
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