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We show that the gradient flow u on L2 generated by the energy functional I(u ): =  U Φ(det Du) dx for vector-valued mappings is in some sense "integrable", meaning that (i) the inverse Jacobian β := (det Du)−1 satisfies a scalar nonlinear diffusion equation, and (ii) we can recover u by solving an ODE determined by β.

Diffeomorphisms and Nonlinear Heat Flows