Definition:Harmonic Function/Riemannian Manifold

Definition
Let $\struct {M, g}$ be a compact Riemannian manifold with or without boundary.

Let $\map {\CC^\infty} M$ be the smooth function space.

Let $u \in \map {\CC^\infty} M$ be a smooth real function on $M$.

Let $\Delta$ be the Laplacian.

Then $u$ is said to be harmonic if $\Delta u = 0$