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.
Nonexistence of horizontal Sobolev surfaces in the Heisenberg group
MAGNANI, VALENTINO
2010-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
