1301.0739 (Colette Anné et al.)

The Gauß-Bonnet operator of an infinite graph    [PDF]

Colette Anné, Nabila Torki-Hamza

We propose a general condition for selfadjointness of the Gau{\ss}-Bonnet operator D=d+delta based on the notion of negligible boundary introduced by Gaffney. This gives self-adjointness of the Laplace operator both for functions or 1-forms on infinite graphs. This is used to extend Flanders result concerning solutions of Kirchhoff laws.

View original: http://arxiv.org/abs/1301.0739