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 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
5 Citations
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#### References

SHOWING 1-10 OF 41 REFERENCES
Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot Groups
A Carnot group G $\mathbb {G}$ is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as ℂ 1 $\mathbbExpand Intrinsic Lipschitz Graphs Within Carnot Groups • Mathematics • 2016 A Carnot group is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study the notions of intrinsic graphs and of intrinsic Lipschitz graphs within Carnot groups.Expand INTRINSIC LIPSCHITZ GRAPHS IN HEISENBERG GROUPS In the last few years there have been a fairly large amount of work dedicated to the study of intrinsic submanifolds of various dimension and codimension inside the Heisenberg groups H or moreExpand Area of intrinsic graphs and coarea formula in Carnot Groups • Mathematics • 2020 We consider submanifolds of sub-Riemannian Carnot groups with intrinsic$C^1$regularity ($C^1_H$). Our first main result is an area formula for$C^1_H$intrinsic graphs; as an application, we deduceExpand Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem • Mathematics • 2014 Abstract A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra.We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within CarnotExpand Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs • Mathematics • 2009 Abstract We continue to study ℍ-regular graphs, a class of intrinsic regular hypersurfaces in the Heisenberg group endowed with a left-invariant metric d ∞ equivalent to its Carnot–CarathéodoryExpand Universal differentiability sets and maximal directional derivatives in Carnot groups • Mathematics • 2017 We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G is Pansu differentiable at some pointExpand Intrinsic regular surfaces of low codimension in Heisenberg groups In this paper we study intrinsic regular submanifolds of$\mathbb{H}^n\$, of low co-dimension in relation with the regularity of their intrinsic parametrization. We extend some results proved for oneExpand
Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces
• Mathematics
• 2019
This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces inExpand
Intrinsic Difference Quotients
An alternative characterizations of intrinsic Lipschitz functions within Carnot groups through the boundedness of appropriately defined difference quotients is provided. It is also shown howExpand