Analysis and Geometry on Graphs and Manifolds

doi:10.1017/9781108615259

The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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List of Contributors
pp vii-x
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Preface
pp xi-xiv
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1 - Infinite Planar Graphs with Non-negative Combinatorial Curvature
pp 1-20
- By Bobo Hua, Yanhui Su
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2 - Curvature Calculations for Antitrees
pp 21-54
- By David Cushing,, Shiping Liu, Florentin Münch, Norbert Peyerimhoff
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3 - Gromov–Lawson Tunnels with Estimates
pp 55-65
- By Józef Dodziuk
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4 - Norm Convergence of the Resolvent for Wild Perturbations
pp 66-75
- By Colette Anné, Olaf Post
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5 - Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
pp 76-94
- By Christian Rose, Peter Stollmann
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6 - Multiple Boundary Representations of λ-Harmonic Functions on Trees
pp 95-125
- By Massimo A. Picardello, Wolfgang Woess
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7 - Internal DLA on Sierpinski Gasket Graphs
pp 126-155
- By Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss, Alexander Teplyaev
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8 - Universal Lower Bounds for Laplacians on Weighted Graphs
pp 156-171
- By D. Lenz, P. Stollmann
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9 - Critical Hardy Inequalities on Manifolds and Graphs
pp 172-202
- By Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
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10 - Neumann Domains on Graphs and Manifolds
pp 203-249
- By Lior Alon, Ram Band, Michael Bersudsky, Sebastian Egger
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11 - On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
pp 250-327
- By Marcel Schmidt
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12 - Box Spaces: Geometry of Finite Quotients
pp 328-343
- By Ana Khukhro, Alain Valette
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13 - Ramanujan Graphs and Digraphs
pp 344-367
- By Ori Parzanchevski
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14 - From Partial Differential Equations to Groups
pp 368-381
- By Andrzej Zuk
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15 - Spectral Properties of Limit-Periodic Operators
pp 382-444
- By David Damanik, Jake Fillman
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16 - Uniform Existence of the IDS on Lattices and Groups
pp 445-478
- By C. Schumacher, F. Schwarzenberger, I. Veselić
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Analysis and Geometry on Graphs and Manifolds

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

List of Contributors
pp vii-x

Preface
pp xi-xiv

1 - Infinite Planar Graphs with Non-negative Combinatorial Curvature
pp 1-20

2 - Curvature Calculations for Antitrees
pp 21-54

3 - Gromov–Lawson Tunnels with Estimates
pp 55-65

4 - Norm Convergence of the Resolvent for Wild Perturbations
pp 66-75

5 - Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
pp 76-94

6 - Multiple Boundary Representations of λ-Harmonic Functions on Trees
pp 95-125

7 - Internal DLA on Sierpinski Gasket Graphs
pp 126-155

8 - Universal Lower Bounds for Laplacians on Weighted Graphs
pp 156-171

9 - Critical Hardy Inequalities on Manifolds and Graphs
pp 172-202

10 - Neumann Domains on Graphs and Manifolds
pp 203-249

11 - On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators
pp 250-327

12 - Box Spaces: Geometry of Finite Quotients
pp 328-343

13 - Ramanujan Graphs and Digraphs
pp 344-367

14 - From Partial Differential Equations to Groups
pp 368-381

15 - Spectral Properties of Limit-Periodic Operators
pp 382-444

16 - Uniform Existence of the IDS on Lattices and Groups
pp 445-478

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Analysis and Geometry on Graphs and Manifolds

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