Traveling waves for reaction-diffusion equations involving the curvature operator

We are concerned with the existence of monotone traveling waves which connect two equilibria for a reaction-diffusion PDE where the spatial diffusion is of mean-curvature type. We study the set of the admissible speeds (i.e., the numbers c for which there exists a traveling wave as above with speed c) for different kinds of reaction terms, showing analogies and differences with respect to the linear diffusion case. The technique used relies on a change of variables leading to a suitable first order reduction.