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

@article{Antonelli2020CharacterizationsOU, title={Characterizations of uniformly differentiable co-horizontal intrinsic graphs in Carnot groups}, author={Gioacchino Antonelli and Daniela Di Donato and Sebastiano Don and Enrico Le Donne}, journal={arXiv: Metric Geometry}, year={2020} }

In arbitrary Carnot groups we study intrinsic graphs of maps with horizontal target. These graphs are $C^1_H$ regular exactly when the map is uniformly intrinsically differentiable. Our first main result characterizes the uniformly intrinsic differentiability by means of Holder properties along the projections of left-invariant vector fields on the graph. We strengthen the result in step-2 Carnot groups for intrinsic real-valued maps by only requiring horizontal regularity. We remark that such… Expand

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