## 15 Citations

### Geometric and Spectral Consequences of Curvature Bounds on Tessellations

- Mathematics
- 2017

This chapter focuses on geometric and spectral consequences of curvature bounds. Several of the results presented here have analogues in Riemannian geometry but in some cases one can go even beyond…

### Eigenvalue asymptotics and unique continuation of eigenfunctions on planar graphs

- Mathematics
- 2021

We study planar graphs with large negative curvature outside of a finite set and the spectral theory of Schrödinger operators on these graphs. We obtain estimates on the first and second order term…

### Banach spaces-valued ergodic theorems and spectral approximation

- Mathematics
- 2014

The present dissertation thesis is concerned with Banach space-valued convergence theorems along Folner type sequences in geometries with amenable structures. The text contains new ergodic theorems…

### On the largest planar graphs with everywhere positive combinatorial curvature

- MathematicsJournal of Combinatorial Theory, Series B
- 2023

### Bakry–Émery curvature and diameter bounds on graphs

- Mathematics
- 2016

We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and maximal vertex degree is sharp in the…

### A note on the surjectivity of operators on vector bundles over discrete spaces

- MathematicsArchiv der Mathematik
- 2019

In this note we give a short and self-contained proof for a criterion of Eidelheit on the solvability of linear equations in infinitely many variables. We use this criterion to study the surjectivity…

### A note on the surjectivity of operators on vector bundles over discrete spaces

- MathematicsArchiv der Mathematik
- 2019

In this note we give a short and self-contained proof for a criterion of Eidelheit on the solvability of linear equations in infinitely many variables. We use this criterion to study the surjectivity…

### UNIQUE CONTINUATION PRINCIPLES AND THEIR ABSENCE FOR SCHRöDINGER EIGENFUNCTIONS ON COMBINATORIAL AND QUANTUM GRAPHS AND IN CONTINUUM SPACE

- Mathematics
- 2017

For the analysis of the Schrodinger and related equations it is of central importance whether a unique continuation principle (UCP) holds or not. In continuum Euclidean space, quantitative forms of…

### The Kazdan–Warner equation on canonically compactifiable graphs

- Mathematics
- 2017

We study the Kazdan–Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians…

## References

SHOWING 1-10 OF 67 REFERENCES

### Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature II

- Mathematics
- 2011

In the present paper, we apply Alexandrov geometry methods to study geometric analysis aspects of infinite semiplanar graphs with nonnegative combinatorial curvature in the sense of Higuchi. We…

### Bochner's Method for Cell Complexes and Combinatorial Ricci Curvature

- MathematicsDiscret. Comput. Geom.
- 2003

A combinatorial analogue of Bochner's theorems is derived, which demonstrates that there are topological restrictions to a space having a cell decomposition with everywhere positive curvature.

### Curvature, Geometry and Spectral Properties of Planar Graphs

- MathematicsDiscret. Comput. Geom.
- 2011

It is shown that non-positive curvature implies that the graph is infinite and locally similar to a tessellation, and a characterization for triviality of the essential spectrum by uniform decrease of the curvature is given.

### Coherence and negative sectional curvature in complexes of groups

- Mathematics
- 2013

We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which…

### Polygonal complexes and combinatorial group theory

- Mathematics
- 1994

We study the structure of certain simply connected 2-dimensional complexes with non-positive curvature. We obtain a precise description of how these complexes behave at infinity and prove an…

### CHEEGER ISOPERIMETRIC CONSTANTS OF GROMOV-HYPERBOLIC SPACES WITH QUASI-POLES

- Mathematics
- 2000

Let X be a non-compact complete manifold (or a graph) which admits a quasi-pole and has bounded local geometry. Suppose that X is Gromov-hyperbolic and the diameters (for a fixed Gromov metric) of…

### A CHARACTERIZATION OF HYPERBOLIC SPACES

- Mathematics
- 2004

We show that a geodesic metric space, and in particular the Cayley graph of a finitely generated group, is hyperbolic in the sense of Gromov if and only if intersections of any two metric balls is…

### Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature

- Mathematics
- 2004

This paper is concerned with elliptic operators on plane tessellations. We show that such an operator does not admit a compactly supported eigenfunction if the combinatorial curvature of the…

### Metric Spaces of Non-Positive Curvature

- Mathematics
- 1999

This book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by…

### Ricci curvature and eigenvalue estimate on locally finite graphs

- Mathematics
- 2010

We give a generalizations of lower Ricci curvature bound in the framework of graphs. We prove that the Ricci curvature in the sense of Bakry and Emery is bounded below by $-1$ on locally finite…