Calculus of Variations and Geometric Measure Theory

V. Magnani

Nonexistence of horizontal Sobolev surfaces in the Heisenberg group

created by magnani on 12 Mar 2009
modified on 10 Jan 2012


Published Paper

Inserted: 12 mar 2009
Last Updated: 10 jan 2012

Journal: Proc. Amer. Math. Soc.
Volume: 138
Number: 5
Pages: 1785–1791
Year: 2010


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, J.T.Tyson.

Keywords: Heisenberg group, Sobolev surfaces, Involutivity, Nonintegrable distributions