# A Weil–Petersson type metric on spaces of metric graphs

@article{Pollicott2014AWT, title={A Weil–Petersson type metric on spaces of metric graphs}, author={Mark Pollicott and Richard Sharp}, journal={Geometriae Dedicata}, year={2014}, volume={172}, pages={229-244} }

In this note, we discuss an analogue of the Weil–Petersson metric for spaces of metric graphs and some of its properties.

## 17 Citations

### Pressure type metrics on spaces of metric graphs

- Mathematics
- 2016

In this note, we consider two Riemannian metrics on a moduli space of metric graphs. Each of them could be thought of as an analogue of the Weil–Petersson metric on the moduli space of metric graphs.…

### Entropy and the clique polynomial

- Mathematics
- 2015

This paper gives a sharp lower bound on the spectral radius ρ(A) of a reciprocal Perron–Frobenius matrix A∈M2g(Z) , and shows in particular that ρ(A)g⩾(3+5)/2 . This bound supports conjectures on the…

### Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space

- Mathematics
- 2014

We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection…

### Incompleteness of the pressure metric on the Teichmüller space of a bordered surface

- MathematicsErgodic Theory and Dynamical Systems
- 2017

We prove that the pressure metric on the Teichmüller space of a bordered surface is incomplete and that a completion can be given by the moduli space of metrics on a graph (dual to a special ideal…

### Pressure metrics for deformation spaces of quasifuchsian groups with parabolics

- Mathematics
- 2020

In this paper, we produce a mapping class group invariant pressure metric on the space QF(S) of quasiconformal deformations of a co-finite area Fuchsian group uniformizing a surface S. Our pressure…

### The geometry of the Weil-Petersson metric in complex dynamics

- Mathematics
- 2015

In this work, we study an analogue of the Weil-Petersson metric on the space of Blaschke products of degree 2 proposed by McMullen. Via the Bers embedding, one may view the Weil-Petersson metric as a…

### Entropy and the clique polynomial The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters

- Mathematics
- 2014

This paper gives a sharp lower bound on the spectral radius ρ ( A ) of a reciprocal Perron–Frobenius matrix A ∈ M 2 g ( Z ), and shows in particular that ρ ( A ) g ≥ (3 + √ 5) / 2. This bound…

### Thermodynamic metrics on outer space

- Mathematics, Computer ScienceErgodic Theory and Dynamical Systems
- 2022

The entropy metric and the pressure metric are considered, which can be seen as analogs of the Weil–Petersson metric on the Teichmüller space of a closed surface and it is shown that when the rank r is at least 4, the action of r on the completion of the Culler–Vogtmann outer space using the entropy metric has a fixed point.

### Conformally covariant operators and conformal invariants on weighted graphs

- Mathematics
- 2014

Let $$G$$G be a finite connected simple graph. We define the moduli space of conformal structures on $$G$$G. We propose a definition of conformally covariant operators on graphs, motivated by Graham…

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