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Nonexistence of horizontal Sobolev surfaces in the Heisenberg group


Author: Valentino Magnani
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
Published electronically: December 3, 2009
MathSciNet review: 2587463
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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.


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Additional Information

Valentino Magnani
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy
Email: magnani@dm.unipi.it

DOI: https://doi.org/10.1090/S0002-9939-09-10211-3
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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