A $C^m$ Whitney extension theorem for horizontal curves in the Heisenberg group
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- by Andrea Pinamonti, Gareth Speight and Scott Zimmerman PDF
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Abstract:
We characterize those mappings from a compact subset of $\mathbb {R}$ into the Heisenberg group ${\mathbb {H}}^{n}$, which can be extended to a $C^{m}$ horizontal curve in $\mathbb {H}^{n}$. The characterization combines the classical Whitney conditions with an estimate comparing changes in the vertical coordinate with those predicted by the Taylor series of the horizontal coordinates.References
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Additional Information
- Andrea Pinamonti
- Affiliation: Department of Mathematics, University of Trento, Via Sommarive 14, 38123 Povo (Trento), Italy
- MR Author ID: 997336
- Email: Andrea.Pinamonti@unitn.it
- Gareth Speight
- Affiliation: Department of Mathematical Sciences, University of Cincinnati, 2815 Commons Way, Cincinnati, Ohio 45221
- MR Author ID: 1003655
- Email: Gareth.Speight@uc.edu
- Scott Zimmerman
- Affiliation: Department of Mathematics, University of Connecticut, 341 Mansfield Road U1009, Storrs, Connecticut 06269
- Email: Scott.Zimmerman@uconn.edu
- Received by editor(s): July 20, 2018
- Received by editor(s) in revised form: January 12, 2019
- Published electronically: March 26, 2019
- Additional Notes: Part of this work was done while the first author was visiting the University of Cincinnati. This visit was partly supported by a Research Support Grant from the Taft Research Center at the University of Cincinnati.
The work of the second author was supported by a grant from the Simons Foundation (#576219). - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 8971-8992
- MSC (2010): Primary 53C17; Secondary 54C20
- DOI: https://doi.org/10.1090/tran/7806
- MathSciNet review: 3955570