Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
- 2 Curvature Calculations for Antitrees
- 3 Gromov–Lawson Tunnels with Estimates
- 4 Norm Convergence of the Resolvent for Wild Perturbations
- 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
- 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees
- 7 Internal DLA on Sierpinski Gasket Graphs
- 8 Universal Lower Bounds for Laplacians on Weighted Graphs
- 9 Critical Hardy Inequalities on Manifolds and Graphs
- 10 Neumann Domains on Graphs and Manifolds
- 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
- 12 Box Spaces: Geometry of Finite Quotients
- 13 Ramanujan Graphs and Digraphs
- 14 From Partial Differential Equations to Groups
- 15 Spectral Properties of Limit-Periodic Operators
- 16 Uniform Existence of the IDS on Lattices and Groups
2 - Curvature Calculations for Antitrees
Published online by Cambridge University Press: 14 August 2020
Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
- 2 Curvature Calculations for Antitrees
- 3 Gromov–Lawson Tunnels with Estimates
- 4 Norm Convergence of the Resolvent for Wild Perturbations
- 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
- 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees
- 7 Internal DLA on Sierpinski Gasket Graphs
- 8 Universal Lower Bounds for Laplacians on Weighted Graphs
- 9 Critical Hardy Inequalities on Manifolds and Graphs
- 10 Neumann Domains on Graphs and Manifolds
- 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
- 12 Box Spaces: Geometry of Finite Quotients
- 13 Ramanujan Graphs and Digraphs
- 14 From Partial Differential Equations to Groups
- 15 Spectral Properties of Limit-Periodic Operators
- 16 Uniform Existence of the IDS on Lattices and Groups
Summary
In this article we prove that antitrees with suitable growth properties are examples of infinite graphs exhibiting strictly positive curvature in various contexts: in the normalized and non-normalized Bakry-Émery setting as well in the Ollivier-Ricci curvature case. We also show that these graphs do not have global positive lower curvature bounds, which one would expect in view of discrete analogues of the Bonnet-Myers theorem. The proofs in the different settings require different techniques.
- Type
- Chapter
- Information
- Analysis and Geometry on Graphs and Manifolds , pp. 21 - 54Publisher: Cambridge University PressPrint publication year: 2020
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