(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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The Geometric Heat Equation-WTF?

**Physics Forums | Science Articles, Homework Help, Discussion**