(adsbygoogle = window.adsbygoogle || []).push({}); The Geometric Heat Equation--WTF??

I need some help getting from point A to B. Let's say we have the plain ol' heat equation

[tex]u_t=\Delta u[/tex]

where the [tex]u=u\left(x,t\right)[/tex], and that's all good. Then, we also have the so-called geometric heat equation

[tex]\dfrac{\partial F}{\partial t}=kN[/tex]

where [tex]F:\mathcal{M}\rightarrow\mathcal{M}'[/tex] is a smooth map between btween Riemannian manifolds, [tex]k[/tex] the curvature, and [tex]N[/tex] the unit normal vector. Intuitivly, I can see how these are the same, but I cannot seem to work out how to go from [tex]\Delta[/tex] to [tex]kN[/tex].

Of course, I can explain my woes further if anyone has any ideas, so let me know what you all think. Thanks!

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# The Geometric Heat Equation-WTF?

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