A note on the quantum-mechanical Ricci flow
  We obtain Schroedinger quantum mechanics from Perelman's functional and from the Ricci flow equations of a conformally flat Riemannian metric on a closed 2-dimensional configuration space. We explore links with the recently discussed "emergent quantum mechanics". 
J.M. Isidro, J.L.G. Santander, P. Fernandez de Cordoba