Complete non-compact submanifolds in Euclidean space with L^p-integrable second fundamental form (p > n) have essential spectrum [0, +∞).
Kumura, On the essential spectrum of the Laplacian and vague convergence of the curvature at infinity, Commun
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Spectral Bernstein theorems for submanifolds in Euclidean spaces
Complete non-compact submanifolds in Euclidean space with L^p-integrable second fundamental form (p > n) have essential spectrum [0, +∞).