 Nonnegativity of the Hodge Laplacian

ID: nonnegativity-of-the-hodge-laplacian

Codex  0 Created 2026-10-03 Updated 2026-10-05

On a compact oriented Riemannian manifold without boundary, the codifferential is the

L^{2}

⟨ Δ α, α ⟩_{L^{2}} = ∥ d α ∥_{L^{2}}^{2} + ∥ δ α ∥_{L^{2}}^{2} \geq 0.

Every eigenvalue of the Hodge Laplacian is therefore nonnegative.

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