IUMJ

Title: Horizontal Gauss curvature flow of graphs in Carnot groups

Authors: Erin Haller Martin

Issue: Volume 60 (2011), Issue 4, 1267-1302

Abstract:

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 $\mathbb{G}$.