Friday, January 11, 2013

1301.2202 (Yajun Zhou)

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

Yajun Zhou
A simple formula is derived for the Ricci scalar curvature of any smooth level set ${\psi(x_0,x_1,...,x_n)=C}$ embedded in the Euclidean space $ \mathbb R^{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.
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