Is this what you suggest:
s = \int \sqrt{ 1 + (\frac{dy}{dx})^2} dx
for constant g we have furthermore:
g(x,y) = t = const \Rightarrow
g_x + g_y \frac{dy}{dx} = 0
and, thus,
s = \int \sqrt{ 1 + (g_x/g_y)^2} dx
The jacobian determinant is
J = 1/(\left| g_x s_y...
I am agonizing about the following integral identity:
\frac{d}{dt} \int \int_{g(x,y) \leq t} f(x,y) dx dy = \int_{g(x,y)=t} f(x,y) \frac{1}{\left| \nabla g(x,y) \right|} ds,
where ds is the line element. Clearly, using the Heavisite step function, the condition g(x,y) \leq t is...