Analysis and Geometry on Graphs and Manifolds (London Mathematical Society Lecture Note Series (Series Number 461))

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. Contents 6 List of Contributors 8 Preface 12 1 Infinite Planar Graphs with Non-negative Combinatorial Curvature 16 2 Curvature Calculations for Antitrees 36 3 Gromov–Lawson Tunnels with Estimates 70 4 Norm Convergence of the Resolvent for Wild Perturbations 81 5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications 91 6 Multiple Boundary Representations of λ-Harmonic Functions on Trees 110 7 Internal DLA on Sierpinski Gasket Graphs 141 8 Universal Lower Bounds for Laplacians on Weighted Graphs 171 9 Critical Hardy Inequalities on Manifolds and Graphs 187 10 Neumann Domains on Graphs and Manifolds 218 11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators 265 12 Box Spaces: Geometry of Finite Quotients 343 13 Ramanujan Graphs and Digraphs 359 14 From Partial Differential Equations to Groups 383 15 Spectral Properties of Limit-Periodic Operators 397 16 Uniform Existence of the IDS on Lattices and Groups 460 "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"-- Provided by publisher This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics