Nonexistence of horizontal Sobolev surfaces in the Heisenberg group
Analysis of PDEs
2009-03-13 v1 Differential Geometry
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 \H^1. Here we answer a question raised in a paper by Z.M.Balogh, R.Hoefer-Isenegger, J.T.Tyson.
Keywords
Cite
@article{arxiv.0903.2214,
title = {Nonexistence of horizontal Sobolev surfaces in the Heisenberg group},
author = {Valentino Magnani},
journal= {arXiv preprint arXiv:0903.2214},
year = {2009}
}