Corpus ID: 218870254

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 D. 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