# 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.

## 16 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…

An introduction to pressure metrics for higher Teichmüller spaces

- MathematicsErgodic Theory and Dynamical Systems
- 2017

We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichmüller spaces. Our higher Teichmüller spaces will be spaces of Anosov representations of a word-hyperbolic group…

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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