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E-raamat: Analysis and Geometry on Graphs and Manifolds

Edited by , Edited by (Universität Potsdam, Germany), Edited by (Universität Potsdam, Germany)
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Analysis and Geometry on Graphs and ManifoldsSuurem pilt
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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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A contemporary exploration of the interplay between geometry, spectral theory and stochastics which is explored for graphs and manifolds.
List of Contributors
vii
Preface xi
1 Infinite Planar Graphs with Non-negative Combinatorial Curvature
1(20)
Bobo Hua
Yanhui Su
2 Curvature Calculations for Antitrees
21(34)
David Cushing
Shiping Liu
Florentin Munch
Norbert Peyer-imhoff
3 Gromov-Lawson Tunnels with Estimates
55(11)
Jozef Dodziuk
4 Norm Convergence of the Resolvent for Wild Perturbations
66(10)
Colette Anni
Olaf Post
5 Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
76(19)
Christian Rose
Peter Stollmann
6 Multiple Boundary Representations of A.-Harmonic Functions on Trees
95(31)
Massimo A. Picardello
Wolfgang Woess
7 Internal DLA on Sierpinski Gasket Graphs
126(30)
Joe P. Chen
Wilfried Huss
Ecaterina Sava-Huss
Alexander Teplyaev
8 Universal Lower Bounds for Laplacians on Weighted Graphs
156(16)
D. Lenz
P. Stollmann
9 Critical Hardy Inequalities on Manifolds and Graphs
172(31)
Matthias Keller
Yehuda Pinchover
Felix Pogorzelski
10 Neumann Domains on Graphs and Manifolds
203(47)
Lior Alon
Ram Band
Michael Bersudsky
Sebastian Egger
11 On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrodinger Operators
250(78)
Marcel Schmidt
12 Box Spaces: Geometry of Finite Quotients
328(16)
Ana Khukhro
Alain Valette
13 Ramanujan Graphs and Digraphs
344(24)
Ori Parzanchevski
14 From Partial Differential Equations to Groups
368(14)
Andrzej Zuk
15 Spectral Properties of Limit-Periodic Operators
382(63)
David Damanik
Jake Fillman
16 Uniform Existence of the IDS on Lattices and Groups
445
C. Schumacher
F. Schwarzenberger
I. Veselid
Matthias Keller is a Professor of Mathematics at the University of Potsdam. He has contributed to books including Random Walks, Boundaries and Spectra (2011) and Modern Approaches to Discrete Curvature (2017). Daniel Lenz is a Professor of Mathematics at the Friedrich-Schiller University Jena. He has written numerous papers and previously contributed to Groups, Graphs and Random Walks (Cambridge, 2017). Radoslaw K. Wojciechowski is an Associate Professor at the City University of New York and a member of the American Mathematical Society. He currently has a Simons Collaboration Grant for Mathematicians and previously was awarded a National Science Foundation Conferences and Workshops in the Mathematical Sciences Grant. He has contributed to the book Random Walks, Boundaries and Spectra (2011).
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