Characterizations of uniformly differentiable co-horizontal intrinsic graphs in Carnot groups

In arbitrary Carnot groups we study intrinsic graphs of maps with horizontal target. These graphs are C H 1 regular exactly when the map is uniformly intrinsically differentiable. Our first main result characterizes the uniformly intrinsic differentiability by means of Hölder properties along the projections of left-invariant vector fields on the graph.