  Although the Poincare' and the geometrization conjectures were recently
proved by Perelman, the proof relies heavily on properties of the Ricci flow
previously investigated in great detail by Hamilton. Physical realization of
such a flow can be found, for instance, in the work by Friedan
(Ann.Phys.163(1985)318-419). In his work the renormalization group flow for a
nonlinear sigma model in 2+e dimensions was obtained and studied. For e=0, by
approximating the beta function for such a flow by the lowest order terms in
the sigma model coupling constant, the equations for Ricci flow are obtained.
In view of such an approximation, the existence of this type of flow in nature
is questionable. In this work, we find totally independent justification for
the existence of Ricci flows in nature. This is achieved by developing a new
formalism extending the results of 2d CFT to 3 and higher dimensions. Equations
describing critical dynamics of these CFT's are examples of the Yamabe and
Ricci flows realizable in nature. Although in the original works by Perelman
some physically motivated arguments can be found, their role in his proof
remain either nonexistent or obscure. In this paper, steps are made toward
making these arguments more explicit thus creating an opportunity for
developing alternative, more physically motivated, proofs of the Poincare' and
geometrization conjectures.
