Horizontal Gauss curvature flow of graphs in Carnot groups Erin Haller Martin 35B5135K6522E25Carnot groupcomparison principlecurvature flowhorizontal Gauss curvatureviscosity solutions We show the existence of continuous viscosity solutions to the equation describing the flow of a graph in the Carnot group $\mathbb{G}\times\mathbb{R}$ according to its horizontal Gauss curvature. In doing so, we prove a comparison principle for degenerate parabolic equations of the form $u_t + F(D_0u,(D_0^2u)^{*}) = 0$ for $u$ defined on $\mathbb{G}$. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4411 10.1512/iumj.2011.60.4411 en Indiana Univ. Math. J. 60 (2011) 1267 - 1302 state-of-the-art mathematics http://iumj.org/access/