# Lipschitz constant of the Laplace-Beltrami operator

I'm reading a paper on discrete differential geometry: Meyer et.al.

They define the Laplace-Beltrami operator at a point $P$ by $$\vec{K}(p) = 2k_H(P)\vec{n(P)}$$ where $\vec{n}(p)$ is the normal vector at $p$ and $k_H(p)$ the mean curvature. Then in Section 3.2 they give an error bound for the discrete Laplace-Beltrami operator obtained in the previous section.

At one step they write $||\vec{K}(x) - \vec{K}(x_i)||^2 \leq C_i^2||x-x_i||^2$ where $C_i$ is the Lipschitz constant of the Laplace-Beltrami operator.

Does anyone have a reference to where I can find a proof that the Laplace-Beltrami operator is Lipschitz (at least for surfaces in $R^3$)?

Thank you.

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mathoverflow.net/questions/65966/… – M.B. May 25 '11 at 14:24