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Nonexistence of horizontal Sobolev surfaces in the Heisenberg group
Author(s):
Valentino
Magnani
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1785-1791.
MSC (2000):
Primary 26B99;
Secondary 28A78, 53C17
Posted:
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  . 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:
10.1090/S0002-9939-09-10211-3
PII:
S 0002-9939(09)10211-3
Received by editor(s):
March 19, 2009,
Received by editor(s) in revised form:
September 11, 2009
Posted:
December 3, 2009
Communicated by:
Mario Bonk
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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