Horizontal Gauss Curvature Flow of Graphs in Carnot Groups
Abstract
We show the existence of continuous viscosity solutions to the equation describing the flow of a graph in the Carnot group G x R according to its horizontal Gauss curvature. In doing so, we prove a comparison principle for degenerate parabolic equations of the form ut + F(D0u, (D02u)*) = 0 for u defined on G.
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