## 11 Citations

### 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…

### 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…

### 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…

### Graphs with large girth and nonnegative curvature dimension condition

- MathematicsCommunications in Analysis and Geometry
- 2019

In this paper, we classify unweighted graphs satisfying the curvature dimension condition CD(0,\infty) whose girth are at least five.

### Sharp isoperimetric inequalities for infinite plane graphs with bounded vertex and face degrees

- Mathematics
- 2020

We give sharp bounds for isoperimetric constants of infinite plane graphs(tessellations) with bounded vertex and face degrees. For example if $G$ is a plane graph satisfying the inequalities $p_1…

### Agmon estimates for Schr\"odinger operators on graphs

- Mathematics
- 2021

We prove decay estimates for generalized eigenfunctions of discrete Schrödinger operators on weighted infinite graphs in the spirit of Agmon. 2000 Mathematics Subject Classification. Primary 39A12,…

### 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…

## References

SHOWING 1-10 OF 97 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…

### Combinatorial curvature for planar graphs

- MathematicsJ. Graph Theory
- 2001

Regarding an infinite planar graph G as a discrete analogue of a noncompact simply connected Riemannian surface, we introduce the combinatorial curvature of G corresponding to the sectional curvature…

### 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…

### Sectional curvature, compact cores, and local quasiconvexity

- Mathematics
- 2004

AbstractWe define a new notion of sectional curvature for 2-complexes,
and describe a variety of examples with nonpositive or negative sectional
curvature. The 2-complexes with nonpositive sectional…