The Gauß-Bonnet operator of an infinite graph

2013/01/04 by Colette Anné, Anné, Colette, Nabila Torki-Hamza +1 · 3 citations
Computer Science · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · doi:10.48550/arxiv.1301.0739

openalex publication_date 2013/01/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We propose a general condition, to ensure essential self-adjointness for the Gauß-Bonnet operator, based on a notion of completeness as Chernoff. This gives essential 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's laws.

Cited by

• Geometric Criteria for Essential Self-Adjointness of Discrete Hodge Laplacians on Weighted Simplicial Complexes
• Essential self-adjointness of non-semibounded Schrödinger operators on infinite graphs
• On Hodge Laplacians on General Simplicial Complexes

Related

• Semi-Fredholmness of the discrete Gauss-Bonnet Operator
• Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions
• Essential self-adjointness for combinatorial Schrödinger operators I- Metrically complete graphs
• A graph theoretical Gauss-Bonnet-Chern Theorem
• Essential self-adjointness of non-semibounded Schrödinger operators on infinite graphs