Complete non-compact submanifolds in Euclidean space with L^p-integrable second fundamental form (p > n) have essential spectrum [0, +∞).
Anderson, The compactification of a minimal submanifold in Euclidean space by the Gauss map, http://www.math.sunysb.edu/ anderson/papers.html, preprint, (1984)
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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, +∞).