THERMODYNAMIC FORMALISM AND GEOMETRIC APPLICATIONS FOR TRANSCENDENTAL MEROMORPHIC AND ENTIRE FUNCTIONS

The paper (a 2020 survey by Mayer–Urbański) states, with citations to BKZ12 and related works, that for topologically hyperbolic meromorphic maps in class B one has Psph(2) ≤ 0 and Bowen’s formula HDhyp(f)=HD(Jr(f))=inf{t>0:Psph(t)≤0}, and also explains existence/independence of spherical pressure for such maps. These claims appear as Proposition 13 and Theorem 48 in the survey and are standard in the literature. The model’s solution gives a direct proof of Psph(2)≤0 via spherical area/Koebe distortion and then cites BKZ and Rempe for the Bowen formula and the equality HDhyp(f)=HD(Jr(f)). The approach in (a) is correct and standard; in (b) the statements match the survey’s theorem. Minor wording imprecision aside (about base-point independence), the model’s argument is consistent with the paper’s results.