Analysis and Geometry on Graphs and Manifolds

A contemporary exploration of the interplay between geometry, spectral theory and stochastics which is explored for graphs and manifolds.

Matthias Keller (Edited by), Daniel Lenz (Edited by), Radoslaw K. Wojciechowski (Edited by)

9781108713184, Cambridge University Press

Paperback / softback, published 20 August 2020

492 pages
22.8 x 15.1 x 2.7 cm, 0.72 kg

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.

1. Infinite planar graphs with nonnegative combinatorial curvature Bobo Hua and Yanhui Su
2. Curvature calculations for antitrees David Cushing, Shiping Liu, Florentin Munch and Norbert Peyerimho
3. Gromov-Lawson tunnels with estimates Józef Dodziuk
4. Norm convergence of the resolvent for wild perturbations Colette Anné and Olaf Post
5. Manifolds with Ricci curvature in the Kato class: heat kernel bounds and applications Peter Stollmann and Christian Rose
6. Multiple boundary representations of ? – harmonic functions on trees Massimo A. Picardello and Wolfgang Woess
7. Internal DLA on Sierpinski gasket graphs Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss and Alexander Teplyaev
8. Universal lower bounds for Laplacians on weighted graphs Daniel Lenz and Peter Stollmann 9. On Hardy inequalities on graphs and manifolds Matthias Keller, Yehuda Pinchover and Felix Pogorzelski
10. Neumann domains on manifolds and graphs Lior Alon, Michael Bersudsky, Sebastian Egger and Rami Band
11. On the existence and uniqueness of self-adjoint realizations of discrete (magnetic) Schrödinger operators Marcel Schmidt
12. Box spaces: geometry of finite quotients Ana Khukhro and Alain Valette
13. Ramanujan graphs and digraphs Ori Parzanchevski
14. From partial differential equations to groups Andrzej ?uk
15. Spectral properties of limit-periodic operators David Damanik and Jake Fillman
16. Uniform existence of the IDS on lattices and groups Christoph Schumacher, Fabian Schwarzenberger and Ivan Veselic.

Subject Areas: Algebraic geometry [PBMW], Functional analysis & transforms [PBKF]