On the equivalence of derivatives for maps between Carnot groups

Scott Zimmerman

doi:10.3934/cpaa.2025066

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2025, Volume 24, Issue 10: 1962-1972. Doi: 10.3934/cpaa.2025066

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On the equivalence of derivatives for maps between Carnot groups

Scott Zimmerman^1, ,

1.
The Ohio State University, USA

^*Corresponding author: Scott Zimmerman
^*Corresponding author: Scott Zimmerman

Received: December 2024

Early access: May 12, 2025

Published online: May 12, 2025

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Abstract

This paper gives an alternate, elementary proof of a result of Magnani: maps between Carnot groups that preserve horizontal curves and are continuously differential in horizontal directions in the Euclidean sense are continuously Pansu differentiable. This proof contains primarily Euclidean arguments and also reproves a version of Magnani's mean value estimate for continuously Pansu differentiable maps.

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Mathematics Subject Classification: Primary: 30L99; Secondary: 53B40, 35R03.

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References

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