Nonexistence of horizontal Sobolev surfaces in the Heisenberg group
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Abstract:
Involutivity is a well known necessary condition for integrability of smooth tangent distributions. We show that this condition is still necessary for integrability with Sobolev surfaces. We specialize our study to the left invariant horizontal distribution of the first Heisenberg group $\mathbb {H}^1$. Here we answer a question raised in a paper by Z.M. Balogh, R. Hoefer-Isenegger, and J.T. Tyson.References
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Additional Information
- Valentino Magnani
- Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy
- MR Author ID: 688183
- Email: magnani@dm.unipi.it
- Received by editor(s): March 19, 2009
- Received by editor(s) in revised form: September 11, 2009
- Published electronically: December 3, 2009
- Communicated by: Mario Bonk
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1785-1791
- MSC (2000): Primary 26B99; Secondary 28A78, 53C17
- DOI: https://doi.org/10.1090/S0002-9939-09-10211-3
- MathSciNet review: 2587463