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A simple formula is derived for the Ricci scalar curvature of any smoothlevel set ${\psi(x_0,x_1,...,x_n)=C}$ embedded in the Euclidean space $ \mathbbR^{n+1}$, in terms of the gradient $ \nabla\psi$ and the Laplacian $\Delta\psi$. Some applications are given to the geometry of low-dimensional$p$-harmonic functions and high-dimensional harmonic functions.

A Simple Formula for Scalar Curvature of Level Sets in Euclidean Spaces