Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

In this survey we deal with transcendental meromorphic and entire functions. We thoroughly discuss in this context close relations between topological pressure and conformal measures for geometric potentials. For two more special classes of meromorphic functions, namely dynamically semi-regular and those in the class D that have negative spectrum, we then also discuss, by means of the appropriate transfer (or Perron-Frobenius) operator, the corresponding thermodynamic formalism for such potentials. It holds in its full classical version. At the end of the survey we discuss hyperbolic dimension, Bowen's Formula, and real analyticity of Hausdorff dimension.